Kindly note that we have put a lot of effort into researching the best books on Measure Theory subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Measure Theory" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.
1. “Probability Theory and Elements of Measure Theory” by Heinz Bauer  
2. “Probability and Measure” by P Billingsley
“Probability and Measure” Book Review: The book reflects essential concepts and major aspects of probability. It provides a strong base in probability and measure. The chapters of this book are wellstructured, readerfriendly, and describe Brownian motion and ergodic theory in detail. To give better practical knowledge and relatable content to the readers, many applications used to illustrate reallife situations. It contains many problems along with their solutions. The book will be beneficial for the advanced students of mathematics, statistics, and economics as well as the scientists and engineers interested in measure theory and probability.


3. “Introduction to Measure and Probability” by K R Parthasarathy
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“Introduction to Measure and Probability” Book Review: The book is an excellent blend of aesthetic and practical aspects of measure and probability. The chapters of this cover all the major topics related to probability on Boolean algebra, extension of measures, borel maps, integration, measures on product spaces, Hilbert space, weal convergence of probability measures, and invariant measures on groups. The theorem and proofs are described efficiently. For better understanding of the readers, the book contains many exercises and examples. The book will be useful for the undergraduate and graduate students seeking knowledge in measure theory and probability theory.


4. “An Introduction to Measure Theory” by Terrence Tao
“An Introduction to Measure Theory” Book Review: The book aims at introducing the fundamentals of measure theory and integration theory. It begins with a description of Lebesgue measure and Lebesgue integral. Moving further to abstract measure and integration theory, the topics like standard convergence theorems, Fubini’s theorem, and Carathéodory extension theorem are thoroughly explained. The traditional differentiation theorems namely, Lebesgue and Rademacher differentiation theorems are clearly presented. The content of this book is supported with several examples and problemsolving strategies. The book will be suitable for the first graduate course in real analysis.
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5. “Measure Theory” by Donald L Cohn
“Measure Theory” Book Review: The book presents a fair introduction of measure theory, hence making it a basic text for study of functional analysis and probability theory. The initial section of the book covers integration on locally compact Hausdorff spaces, analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. The later chapters describe measuretheoretic probability theory, BanachTarski paradox, HenstockKurzweil integral, Daniell integral, and existence of liftings. It is a selfcontained text and rich source of information. The book will be valuable for the advanced undergraduate and graduate students in mathematics.


6. “Measure Theory” by Vladimir I Bogachev
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“Measure Theory” Book Review: The book lays an emphasis on the fundamentals of modern measure theory. The chapters of this book cover all the major topics related to constructions and extensive measures, Lebesgue integral, operation on measures and functions, spaces of measures, and connections between the integral and derivative. The topics and concepts featured in this book are ascended from basic to complex. The content of this book is supported with the help of several exercises along with hints and references. The book will be suitable for a graduate course as well as advanced study in measure theory.


7. “Probability and Measure Theory” by Robert B Ash and Catherine A DoléansDade
“Probability and Measure Theory” Book Review: The book presents basic concepts, fundamental principles, and essential topics of Probability and Measure Theory. The chapters of this book are broadly based on conditional probability and expectation, strong laws of large numbers, martingale theory, central limit theorem, ergodic theory, and Brownian motion. The book also consists of many major topics, necessary in analysis. Each chapter ends with a bunch of problems along with their solutions. The book will be an ideal source for the graduating students of mathematics dealing with probability.
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8. “First Look at Rigorous Probability Theory” by Jeffrey S Rosenthal
“First Look at Rigorous Probability Theory” Book Review: The book aims at presenting probability theory with respect to measure theory. The chapters of this book are wellstructured and comprehensive, featuring many intuitive probabilistic concepts along with the recent developments and scope of further development in probability. The major results featured in this book are clearly explained along with their proofs. The book will be an asset for the graduate students of mathematics, statistics, economics, management, finance, computer science, and engineering.


9. “Measure Theory: Questions and Answers” by George A Duckett  
10. “Measure Theory and Fine Properties of Functions” by Lawrence C Evans and Ronald F Gariepy
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“Measure Theory and Fine Properties of Functions” Book Review: The book covers all the essential aspects of measure theory and aims at providing suitable concepts for characterization of the fine properties of sets and functions. The chapters of this describe all the major topics of general measure theory, Hausdorf measure, area and coarea formulas, Sobolev functions, BV functions, sets of finite perimeter, and differentiability and approximation. The Besicovitch’s Covering Theorem, Rademacher’s Theorem, and Alexandro’s Theorem are discussed in detail. The book will be suitable for graduate students in applied mathematics as well as applied mathematicians.


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