Kindly note that we have put a lot of effort into researching the best books on Measure and Integration 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 and Integration" 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. “An Introduction to Measure and Integration” by Inder K Rana
“An Introduction to Measure and Integration” Book Review: The book presents an introduction to Real Analysis, Lebesgue Measure and Integration, Measure Theory, Modern Analysis, Advanced Analysis, and more. First, it gives a detailed review of Riemann Integral and its properties. Then, it discusses two different approaches for extending the notion for Riemann Integral. Next, it deals with the extension of measures and construction of integral in general setting with Lebesgue Measure. Complete proof for the fundamental theorem of calculus for Lebesgue Integral has been given. It then extends the concept of integral to complex valued functions. Later chapters discuss RadonNikodym theorem and the additive set functions.


2. “Lebesgue Measure and integration” by Jain P K
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“Lebesgue Measure and integration” Book Review: This book is a basic course in Lebesgue Measure and Integration for the Honours and PG students. It starts with discussing basic concepts and results which are then taken for granted later in the book. It contains various solved and unsolved examples, remarks, notes, references for indepth learning. It gives detailed explanations of the methods used together with counter examples. Topics such as Infinite Sets, Measurable Sets, Measurable Functions, Lebesgue Integral, Differentiation and Integration and the Lebesgue LpSpaces have been covered.


3. “Measure Theory and Integration” by De Barra G
“Measure Theory and Integration” Book Review: This book approaches integration via measure, rather than measure via integration. This approach makes the ideas easier for the reader to grasp. The proofs of the mathematics involved are given in detail yet a simple manner. Worked examples, statements of results of theorems, exercises with solutions given in the end, all help in thorough learning. This book is useful for students of measure theory and analysis and useful as a reference for the general practitioner. It provides a basic course in Lebesgue Measure and Integration. It gives essential results on differentiation functions of bounded variation. It introduces the reader to convergence in measure. It also emphasises on LebesgueStieltjes integrals.
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4. “Real Analysis: Measure Theory, Integration, and Hilbert Spaces” by Elias M Stein
“Real Analysis: Measure Theory, Integration, and Hilbert Spaces” Book Review: This book presents the core areas of analysis in an integrated manner. It simplifies the unity that exists between the various parts of the subject. It also depicts the wide applicability of ideas of analysis to other fields of mathematics and science. The focus has been put on the development of measure and integration theory, differentiation and integration, Hilbert spaces and Hausdorff measure and fractals. The elements of Hibert space, via the L2 theory have been stated. The book demonstrates these concepts from Fourier analysis, partial differential equations and complex analysis. Finally, the book covers fractionaldimensional sets, including Hausdorff measure, selfreplicating sets, spacefilling curves and Besicovitch sets.


5. “General Measure and Integration” by P K Jain  
6. “The Elements of Integration and Lebesque Measure” by Robert G. Bartle
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“The Elements of Integration and Lebesgue Measure” Book Review: This book consists of two parts. The first part, ‘The Elements of Integration’ presents the chief results of Lebesgue Theory of Integration to a reader. The topics discussed are Decomposition of Measures, Generation of Measures, Modes of Convergence, etc. The second part, ‘The Elements of Lebesgue Measure’ ascertains the reader with theory of Lebesgue Measure in the space Rp. It uses the abstract measure space approach which strikes directly towards the convergence theorems. Thus it helps students of probability, statistics and analysis. Some other topics covered under this part are Examples of Measurable Sets, Approximation of Measurable Sets, Additivity and Nonadditivity, etc.


7. “Measure and Integration” by Gupta  
8. “Measure Theory and Integration” by A K Malik and S K Gupta
“Measure Theory and Integration” Book Review: The book first starts off with the historical development of the notion of set theory and integral theory. Thus it explains Lebesgue Integral, where abstract integration is developed via the measure theory. Topics like the Outer Measure, Cantor’s Ternary Set, Measurable Function, the Lebesgue Integral, Fundamental Theorem of Calculus, Lpspaces, Fubini’s Theorem, the RadonNikodym Theorem, and so on are discussed. The table of contents also include Countability of Sets, Lebesgue Measure, Differentiation and Integration, Product and Signed Measures. The concepts in this book have been taught with the help of motivating examples, probing questions and numerous exercises. The book is flooded with examples, theorems, recapitulations, multiple choice questions, true/false questions and fillintheblanks questions for indepth learning.
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9. “Real Analysis: Theory Of Measure And Integration” by J Yeh
“Real Analysis: Theory Of Measure And Integration” Book Review: The subject of the book is the theory of measure and integration for which the prerequisite knowledge required is advanced calculus. To begin with, it introduces the concepts of measure and measurable functions. The next chapter treats integration of functions on an arbitrary measure space. Then, it treats the interplay between integration and differentiation on the Lebesgue Measure Space. It also discusses additive set functions to measure. Next, it specializes in integration in the Lebesgue Measure space on Rn. It provides an introduction to Hausdorff measures on Rn. Every concept in this book is described accurately and every theorem is given with detailed proof.


10. “A UserFriendly Introduction to Lebesgue Measure and Integration: 78 (Student Mathematical Library)” by Gail S Nelson
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“A UserFriendly Introduction to Lebesgue Measure and Integration: 78 (Student Mathematical Library)” Book Review: This book covers the aspects of the theory of integration typically associated with the name of Lebesgue, and other related topics. It assumes familiarity with sequences, series, limits, continuity, and compactness at the level of UG course in real analysis. It focuses on measure theory, integration, and Lp spaces. The proofs of the theorems covered are very clear and detailed with many examples. It first summarizes the Riemann integral by Darboux approach. Then, it defines the notion of Lebesgue measure for subsets of Rn. Next, it proves that the measurable subsets of Rn form a σalgebra. The book shows the Lebesgue dominated convergence theorem directly and then uses this to derive Fatou’s lemma and the monotone convergence theorem.


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