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Measure Theory: Second Edition
by Donald L. CohnIntended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings. Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review of essential background material.
Measure Theory and Fine Properties of Functions (Textbooks in Mathematics)
by Lawrence C. EvansThis popular textbook provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space, with emphasis upon the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions.Measure Theory and Fine Properties of Functions, Second Edition includes many interesting items working mathematical analysts need to know, but are rarely taught. Topics covered include a review of abstract measure theory, including Besicovitch’s covering theorem, Rademacher’s theorem (on the differentiability a.e. of Lipschitz continuous functions), the area and coarea formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Aleksandrov’s theorem (on the twice differentiability a.e. of convex functions).The topics are carefully selected, and the proofs are succinct, but complete. This book provides ideal reading for mathematicians and graduate students in pure and applied mathematics. The authors assume readers are at least fairly conversant with both Lebesgue measure and abstract measure theory, and the expository style reflects this expectation. The book does not offer lengthy heuristics or motivation, but as compensation presents all the technicalities of the proofs.This new Second Edition has been updated to provide corrections and minor edits from the previous Revised Edition, with countless improvements in notation, format and clarity of exposition. Also new is a section on the sub differentials of convex functions, and in addition the bibliography has been updated.
Measure Theory and Fine Properties of Functions (Studies In Advanced Mathematics Ser. #5)
by LawrenceCraig EvansThis book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in Mn, lower Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. The text provides complete proofs of many key results omitted from other books, including Besicovitch's Covering Theorem, Rademacher's Theorem (on the differentiability a.e. of Lipschitz functions), the Area and Coarea Formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Alexandro's Theorem (on the twice differentiability a.e. of convex functions).Topics are carefully selected and the proofs succinct, but complete, which makes this book ideal reading for applied mathematicians and graduate students in applied mathematics.
Measure Theory and Fine Properties of Functions, Revised Edition (Textbooks in Mathematics)
by Lawrence Craig Evans Ronald F. GariepyThis book emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. The book covers theorems and differentiation in Rn , Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. This second edition includes countless improvements in notation, format, and clarity of exposition. Also new are several sections describing the p- theorem, weak compactness criteria in L1, and Young measure methods for weak convergence. In addition, the bibliography has been updated.
Measure Theory and Integration (Chapman & Hall/CRC Pure and Applied Mathematics #Vol. 266)
by M. M. RaoSignificantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types-providing a complete and detailed review of every aspect of measure and integration theory using valuable examples, exercises, and applications.With more than 170 references for further investigation of the subject, this Second Editionprovides more than 60 pages of new information, as well as a new chapter on nonabsolute integralscontains extended discussions on the four basic results of Banach spacespresents an in-depth analysis of the classical integrations with many applications, including integration of nonmeasurable functions, Lebesgue spaces, and their propertiesdetails the basic properties and extensions of the Lebesgue-Carathéodory measure theory, as well as the structure and convergence of real measurable functionscovers the Stone isomorphism theorem, the lifting theorem, the Daniell method of integration, and capacity theoryMeasure Theory and Integration, Second Edition is a valuable reference for all pure and applied mathematicians, statisticians, and mathematical analysts, and an outstanding text for all graduate students in these disciplines.
Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control
by N. U. Ahmed Shian WangThis book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach.The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature.This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.
A Measured Approach to Ending Poverty and Boosting Shared Prosperity
by World BankIn 2013, the World Bank Group adopted two new goals to guide its work: ending extreme poverty and boosting shared prosperity. More specifically, the goals are to reduce extreme poverty in the world to less than 3 percent by 2030, and to foster income growth of the bottom 40 percent of the population in each country. While poverty reduction has been a mainstay of the World Bank's mission for decades, the Bank has now set a specific goal and timetable, and for the first time, the Bank has explicitly included a goal linked to ensuring that growth is shared by all. The discussion until now has centered primarily on articulating the new goals. This report, the latest in World Bank's Policy Research Report series, goes beyond that and lays out their conceptual underpinnings, discusses their relative strengths and weaknesses by contrasting them with alternative indicators, and proposes empirical approaches and requirements to track progress towards the goals. The report makes clear that the challenges posed by the World Bank Group's new stance extend not just to the pursuit of these goals but, indeed, to their very definition and empirical content. The report also argues that an improved data infrastructure, consisting of many elements including the collection of more and better survey data, is critical to ensure that progress towards these goals can be measured, and policies to help achieve them can be identified and prioritized.
Measured Tones: The Interplay of Physics and Music, Third Edition
by Ian JohnstonMost books concerned with physics and music take an approach that puts physical theory before application. Consequently, these works tend to dampen aesthetic fascination with preludes burdened by an overabundance of algebraic formulae. In Measured Tones: The Interplay of Physics and Music Third Edition, Ian Johnston a professor of astrophysics and
Measurement
by Paul LockhartPaul Lockhart’s Mathematician’s Lament outlined how we introduce math to students in the wrong way. Measurement explains how math should be done. With plain English and pictures, Lockhart makes complex ideas about shape and motion intuitive and graspable, and offers a solution to math phobia by introducing us to math as an artful way of thinking and living.In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science.Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can “do the math” in a way that brings emotional and aesthetic rewards. Measurement is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work.
Measurement
by Paul LockhartLockhart's Mathematician's Lament outlined how we introduce math to students in the wrong way. Measurement explains how math should be done. With plain English and pictures, he makes complex ideas about shape and motion intuitive and graspable, and offers a solution to math phobia by introducing us to math as an artful way of thinking and living.
The Measurement and Analysis of Housing Preference and Choice
by Henny C.C.H. Coolen Sylvia J.T. Jansen Roland W. GoetgelukWhat are the current trends in housing? Is my planned project commercially viable? What should be my marketing and advertisement strategies? These are just some of the questions real estate agents, landlords and developers ask researchers to answer. But to find the answers, researchers are faced with a wide variety of methods that measure housing preferences and choices. To select and value a valid research method, one needs a well-structured overview of the methods that are used in housing preference and housing choice research. This comprehensive introduction to this field offers just such an overview. It discusses and compares numerous methods, detailing the potential limitation of each one, and it reaches beyond methodology, illustrating how thoughtful consideration of methods and techniques in research can help researchers and other professionals to deliver products and services that are more in line with residents' needs.
Measurement and Evaluation in Human Performance
by James R. Morrow Jr. Allen W. Jackson James G. Disch Dale P. MoodMeasurement and Evaluation in Human Performance, Fourth Edition, paves the way for students and professionals to identify and solve human performance problems in the areas of kinesiology, physical education, health, and fitness. Focusing on the concepts of reliability, objectivity, and validity, the text introduces students to tests and measurements and guides them through statistical decision making and accurate interpretation of data. Measurement and Evaluation in Human Performance, Fourth Edition, is designed with student learning in mind with its practical approach, easy-to-read style, and minimal mathematics. Like previous editions, the text combines introductory algebraic concepts with explanations of reliability and validity to assist students in developing the knowledge and tools to gather and analyze data for decision making. The fourth edition also features many upgrades: • An updated online study guide that incorporates more student activities, computer tasks, and quiz questions to help students comprehend the concepts • A realignment of chapters into four cohesive sections leading from background knowledge and basic statistical concepts to supportive theories and practical application • Greater use of Microsoft Excel to assist with statistical calculations, including an appendix of directions, screen captures, and templates for complex calculations • Inclusion of large sample data sets with each chapter’s online study guide content that help students review concepts and emphasize the value of computer skills in the field of measurement and evaluation • More information on physical activity assessment incorporated into all chapters • A new contributor who lends expertise to teachers and coaches in a chapter addressing performance-based assessment In addition to incorporating use of MS Excel, this edition continues to use Predictive Analysis Software (PASW), previously known as Statistical Package for the Social Sciences (SPSS). These computer applications provide students with the skills to quickly complete time-consuming and difficult calculations for large amounts of data.
Measurement and Probability
by Giovanni Battista RossiMeasurement plays a fundamental role both in physical and behavioral sciences, as well as in engineering and technology: it is the link between abstract models and empirical reality and is a privileged method of gathering information from the real world. Is it possible to develop a single theory of measurement for the various domains of science and technology in which measurement is involved? This book takes the challenge by addressing the following main issues: What is the meaning of measurement? How do we measure? What can be measured? A theoretical framework that could truly be shared by scientists in different fields, ranging from physics and engineering to psychology is developed. The future in fact will require greater collaboration between science and technology and between different sciences. Measurement, which played a key role in the birth of modern science, can act as an essential interdisciplinary tool and language for this new scenario. A sound theoretical basis for addressing key problems in measurement is provided. These include perceptual measurement, the evaluation of uncertainty, the evaluation of inter-comparisons, the analysis of risks in decision-making and the characterization of dynamical measurement. Currently, increasing attention is paid to these issues due to their scientific, technical, economic and social impact. The book proposes a unified probabilistic approach to them which may allow more rational and effective solutions to be reached. Great care was taken to make the text as accessible as possible in several ways. Firstly, by giving preference to as interdisciplinary a terminology as possible; secondly, by carefully defining and discussing all key terms. This ensures that a wide readership, including people from different mathematical backgrounds and different understandings of measurement can all benefit from this work. Concerning mathematics, all the main results are preceded by intuitive discussions and illustrated by simple examples. Moreover, precise proofs are always included in order to enable the more demanding readers to make conscious and creative use of these ideas, and also to develop new ones. The book demonstrates that measurement, which is commonly understood to be a merely experimental matter, poses theoretical questions which are no less challenging than those arising in other, apparently more theoretical, disciplines.
Measurement Data Modeling and Parameter Estimation (Systems Evaluation, Prediction, and Decision-Making)
by Zhengming Wang Dongyun Yi Xiaojun Duan Jing Yao Defeng GuThis book discusses the theories, methods, and application techniques of the measurement data mathematical modeling and parameter estimation. It seeks to build a bridge between mathematical theory and engineering practice in the measurement data processing field so theoretical researchers and technical engineers can communicate. It is organized with abundant materials, such as illustrations, tables, examples, and exercises. The authors create examples to apply mathematical theory innovatively to measurement and control engineering. Not only does this reference provide theoretical knowledge, it provides information on first hand experiences.
Measurement Error: Models, Methods, and Applications (Chapman & Hall/CRC Interdisciplinary Statistics)
by John P. BuonaccorsiOver the last 20 years, comprehensive strategies for treating measurement error in complex models and accounting for the use of extra data to estimate measurement error parameters have emerged. Focusing on both established and novel approaches, Measurement Error: Models, Methods, and Applications provides an overview of the main techniques and illu
Measurement Error and Misclassification in Statistics and Epidemiology: Impacts and Bayesian Adjustments (Chapman & Hall/CRC Interdisciplinary Statistics)
by Paul GustafsonMismeasurement of explanatory variables is a common hazard when using statistical modeling techniques, and particularly so in fields such as biostatistics and epidemiology where perceived risk factors cannot always be measured accurately. With this perspective and a focus on both continuous and categorical variables, Measurement Error and Misclassification in Statistics and Epidemiology: Impacts and Bayesian Adjustments examines the consequences and Bayesian remedies in those cases where the explanatory variable cannot be measured with precision. The author explores both measurement error in continuous variables and misclassification in discrete variables, and shows how Bayesian methods might be used to allow for mismeasurement. A broad range of topics, from basic research to more complex concepts such as "wrong-model" fitting, make this a useful research work for practitioners, students and researchers in biostatistics and epidemiology."
Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition (Chapman & Hall/CRC Monographs on Statistics and Applied Probability)
by Raymond J. Carroll David Ruppert Leonard A. Stefanski Ciprian M. CrainiceanuIt's been over a decade since the first edition of Measurement Error in Nonlinear Models splashed onto the scene, and research in the field has certainly not cooled in the interim. In fact, quite the opposite has occurred. As a result, Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition has been revamped and ex
Measurement in Medicine
by Dirk L. Knol Henrica C. de Vet Caroline B. Terwee Lidwine B. MokkinkThe success of the Apgar score demonstrates the astounding power of an appropriate clinical instrument. This down-to-earth book provides practical advice, underpinned by theoretical principles, on developing and evaluating measurement instruments in all fields of medicine. It equips you to choose the most appropriate instrument for specific purposes. The book covers measurement theories, methods and criteria for evaluating and selecting instruments. It provides methods to assess measurement properties, such as reliability, validity and responsiveness, and interpret the results. Worked examples and end-of-chapter assignments use real data and well-known instruments to build your skills at implementation and interpretation through hands-on analysis of real-life cases. All data and solutions are available online. This is a perfect course book for students and a perfect companion for professionals/researchers in the medical and health sciences who care about the quality and meaning of the measurements they perform.
Measurement, Mathematics and New Quantification Theory (Behaviormetrics: Quantitative Approaches to Human Behavior #16)
by Shizuhiko NishisatoThe purpose of this book is to thoroughly prepare diverse areas of researchers in quantification theory. As is well known, quantification theory has attracted the attention of a countless number of researchers, some mathematically oriented and others not, but all of them are experts in their own disciplines. Quantifying non-quantitative (qualitative) data requires a variety of mathematical and statistical strategies, some of which are quite complicated. Unlike many books on quantification theory, the current book places more emphasis on preliminary requisites of mathematical tools than on details of quantification theory. As such, the book is primarily intended for readers whose specialty is outside mathematical sciences. The book was designed to offer non-mathematicians a variety of mathematical tools used in quantification theory in simple terms. Once all the preliminaries are fully discussed, quantification theory is then introduced in the last section as a simple application of those mathematical procedures fully discussed so far. The book opens up further frontiers of quantification theory as simple applications of basic mathematics.
The Measurement of Association: A Permutation Statistical Approach
by Kenneth J. Berry Janis E. Johnston Paul W. Mielke<p>This research monograph utilizes exact and Monte Carlo permutation statistical methods to generate probability values and measures of effect size for a variety of measures of association. Association is broadly defined to include measures of correlation for two interval-level variables, measures of association for two nominal-level variables or two ordinal-level variables, and measures of agreement for two nominal-level or two ordinal-level variables. Additionally, measures of association for mixtures of the three levels of measurement are considered: nominal-ordinal, nominal-interval, and ordinal-interval measures. Numerous comparisons of permutation and classical statistical methods are presented. <p>Unlike classical statistical methods, permutation statistical methods do not rely on theoretical distributions, avoid the usual assumptions of normality and homogeneity of variance, and depend only on the data at hand. This book takes a unique approach to explaining statistics by integrating a large variety of statistical methods, and establishing the rigor of a topic that to many may seem to be a nascent field. This topic is relatively new in that it took modern computing power to make permutation methods available to those working in mainstream research. <p>Written for a statistically informed audience, it is particularly useful for teachers of statistics, practicing statisticians, applied statisticians, and quantitative graduate students in fields such as psychology, medical research, epidemiology, public health, and biology. It can also serve as a textbook in graduate courses in subjects like statistics, psychology, and biology.</p>
Measurement of Higgs Boson Production Cross Sections in the Diphoton Channel: with the full ATLAS Run-2 Data and Constraints on Anomalous Higgs Boson Interactions (Springer Theses)
by Ahmed Tarek Abouelfadl MohamedThis thesis presents the measurement of the Higgs boson cross section in the diphoton decay channel. The measurement relies on proton-proton collision data at a center-of-mass energy √s = 13 TeV recorded by the ATLAS experiment at the Large Hadron Collider (LHC). The collected data correspond to the full Run-2 dataset with an integrated luminosity of 139 fb-1. The measured cross sections are used to constrain anomalous Higgs boson interactions in the Effective Field Theory (EFT) framework. The results presented in this thesis represent a reduction by a factor 2 of the different photon and jet energy scale and resolution systematic uncertainties with respect to the previous ATLAS publication. The thesis details the calibration of electron and photon energies in ATLAS, in particular the measurement of the presampler energy scale and the estimation of its systematic uncertainty. This calibration was used to perform a measurement of the Higgs boson mass in the H → γγ and H → 4l channels using the 36 fb−1 dataset.
Measurement of Productivity and Efficiency: Theory and Practice
by Professor Robin C. Sickles Professor Valentin ZelenyukMethods and perspectives to model and measure productivity and efficiency have made a number of important advances in the last decade. Using the standard and innovative formulations of the theory and practice of efficiency and productivity measurement, Robin C. Sickles and Valentin Zelenyuk provide a comprehensive approach to productivity and efficiency analysis, covering its theoretical underpinnings and its empirical implementation, paying particular attention to the implications of neoclassical economic theory. A distinct feature of the book is that it presents a wide array of theoretical and empirical methods utilized by researchers and practitioners who study productivity issues. An accompanying website includes methods, programming codes that can be used with widely available software like Matlab, R, and Julia, and test data for many of the productivity and efficiency estimators discussed in the book. It will be valuable to upper-level undergraduates, graduate students, and professionals.
Measurement Theory in Action: Case Studies and Exercises
by Kenneth S Shultz David J. Whitney Michael J ZickarMeasurement Theory in Action, Third Edition, helps readers apply testing and measurement theories and features 22 self-contained modules which instructors can match to their courses. Each module features an overview of a measurement issue and a step-by-step application of that theory. Best Practices provide recommendations for ensuring the appropriate application of the theory. Practical Questions help students assess their understanding of the topic. Students can apply the material using real data in the Exercises, some of which require no computer access, while others involve the use of statistical software to solve the problem. Case Studies in each module depict typical dilemmas faced when applying measurement theory followed by Questions to Ponder to encourage critical examination of the issues noted in the cases. The book’s website houses the data sets, additional exercises, PowerPoints, and more. Other features include suggested readings to further one’s understanding of the topics, a glossary, and a comprehensive exercise in Appendix A that incorporates many of the steps in the development of a measure of typical performance. Updated throughout to reflect recent changes in the field, the new edition also features: Recent changes in understanding measurement, with over 50 new and updated references Explanations of why each chapter, article, or book in each module’s Further Readings section is recommended Instructors will find suggested answers to the book’s questions and exercises; detailed solutions to the exercises; test bank with 10 multiple choice and 5 short answer questions for each module; and PowerPoint slides. Students and instructors can access SPSS data sets; additional exercises; the glossary; and additional information helpful in understanding psychometric concepts. It is ideal as a text for any psychometrics or testing and measurement course taught in psychology, education, marketing, and management. It is also an invaluable reference for professional researchers in need of a quick refresher on applying measurement theory.
Measurement Theory in Action: Case Studies and Exercises, Second Edition
by Kenneth S. Shultz Michael J. Zickar David J. WhitneyThis book helps readers apply testing and measurement theories. Featuring 22 self-standing modules, instructors can pick and choose the ones that are most appropriate for their course. Each module features an overview of a measurement issue and a step-by-step application of that theory. Best practices provide recommendations for ensuring the appropriate application of the theory. Practical questions help students assess their understanding of the topic while the examples allow them to apply the material using real data. Two cases in each module depict typical dilemmas faced when applying measurement theory followed by Questions to Ponder to encourage critical examination of the issues noted in the cases. Each module contains exercises some of which require no computer access while others involve the use of SPSS to solve the problem. The book's website houses the accompanying data sets and more. The book also features suggested readings, a glossary of the key terms, and a continuing exercise that incorporates many of the steps in the development of a measure of typical performance. Updated throughout to reflect recent changes in the field, the new edition also features: --A new co-author, Michael Zickar, who updated the advanced topics and added the new module on generalizability theory (Module 22). -Expanded coverage of reliability (Modules 5 & 6) and exploratory and confirmatory factor analysis (Modules 18 & 19) to help readers interpret results presented in journal articles. -Expanded Web Resources, Instructors will now find: suggested answers to the book's questions and exercises; detailed worked solutions to the exercises; and PowerPoint slides. Students and instructors can access the SPSS data sets; additional exercises; the glossary; and website references that are helpful in understanding psychometric concepts. Part 1 provides an introduction to measurement theory and specs for scaling and testing and a review of statistics. Part 2 then progresses through practical issues related to text reliability, validation, meta-analysis and bias. Part 3 reviews practical issues related to text construction such as the development of measures of maximal performance, CTT item analysis, test scoring, developing measures of typical performance, and issues related to response styles and guessing. The book concludes with advanced topics such as multiple regression, exploratory and confirmatory factor analysis, item response theory (IRT), IRT applications including computer adaptive testing and differential item functioning, and generalizability theory. Ideal as a text for any psychometrics, testing and measurement, or multivariate statistics course taught in psychology, education, marketing and management, professional researchers in need of a quick refresher on applying measurement theory will also find this an invaluable reference.