7 Best Books on Measure Theory

We have compiled a list of the Best Reference Books on Measure Theory, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of Measure Theory Books with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Measure Theory below.

 
1."Probability Theory and Elements of Measure Theory" by Heinz Bauer
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2."An Introduction to Measure Theory" by Terrence Tao
“An Introduction to Measure Theory” Book Review: This book provides an introduction to the fundamental concepts of measure theory and integration theory. It commences with a comprehensive depiction of Lebesgue measure and Lebesgue integral. As the book progresses, it delves into abstract measure and integration theory, elaborating on critical topics such as standard convergence theorems, Fubini’s theorem, and Carathéodory extension theorem. The traditional differentiation theorems, namely, Lebesgue and Rademacher differentiation theorems, are also presented in a lucid manner. Furthermore, the book is furnished with numerous examples and problem-solving strategies to aid comprehension. It is ideally suited for a first graduate course in real analysis.

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3."Measure Theory" by Donald L Cohn
“Measure Theory” Book Review: This book offers a comprehensive introduction to measure theory, making it an essential resource for those studying functional analysis and probability theory. The opening section covers integration on locally compact Hausdorff spaces, as well as analytic and Borel subsets of Polish spaces, and the Haar measures on locally compact groups. The later chapters delve into measure-theoretic probability theory, the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings. With its self-contained approach and wealth of information, this book is a valuable resource for advanced undergraduate and graduate students in mathematics.

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4."Measure Theory" by Vladimir I Bogachev
“Measure Theory” Book Review: The book focuses on the fundamentals of contemporary measure theory, covering major topics related to constructions and extensive measures, Lebesgue integral, operations on measures and functions, spaces of measures, and connections between the integral and derivative. The book gradually progresses from basic to complex topics and concepts. The content is complemented by numerous exercises that come with hints and references. This book is appropriate for both graduate courses and advanced studies in measure theory.

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5."Probability and Measure Theory" by Robert B Ash and Catherine A Doléans-Dade
“Probability and Measure Theory” Book Review: The book offers a comprehensive introduction to the fundamental principles and key topics of Probability and Measure Theory. With a focus on conditional probability and expectation, strong laws of large numbers, martingale theory, central limit theorem, ergodic theory, and Brownian motion, the chapters cover a wide range of essential concepts. Additionally, the book includes important topics in analysis, making it a valuable resource for students of mathematics. Each chapter concludes with a selection of practice problems and their solutions, enhancing the learning experience for readers.

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6."Measure Theory: Questions and Answers" by George A Duckett
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7."Measure Theory and Fine Properties of Functions" by Lawrence C Evans and Ronald F Gariepy
“Measure Theory and Fine Properties of Functions” Book Review: The book offers a comprehensive coverage of the fundamental aspects of measure theory, providing readers with the necessary tools to understand and analyze the fine properties of sets and functions. With in-depth discussions on general measure theory, Hausdorff measure, area and co-area formulas, Sobolev functions, BV functions, sets of finite perimeter, differentiability, and approximation, the chapters encompass all the major topics in the field. Detailed explanations of important theorems such as Besicovitch’s Covering Theorem, Rademacher’s Theorem, and Alexandro’s Theorem are also included. This book will be highly beneficial for graduate students in applied mathematics as well as professionals in the field of applied mathematics.

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We have put a lot of effort into researching the best books on Measure Theory and came out with a recommended list and their reviews. If any more book needs to be added to this list, please email us. We are working on free pdf downloads for books on Measure Theory and will publish the download link here. Fill out this Measure Theory books pdf download" request form for download notification.

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