The Theory of Lebesgue Measure and Integration (ISSN) by S. Hartman (PDF)

Description

The Theory of Lebesgue Measure and Integration deals with the theory of Lebesgue measure and integration and introduces the reader to the theory of real functions. The subject matter comprises concepts and theorems that are now considered classical, including the Yegorov, Vitali, and Fubini theorems. The Lebesgue measure of linear sets is discussed, along with measurable functions and the definite Lebesgue integral.Comprised of 13 chapters, this volume begins with an overview of basic concepts such as set theory, the denumerability and non-denumerability of sets, and open sets and closed sets on the real line. The discussion then turns to the theory of Lebesgue measure of linear sets based on the method of M. Riesz, together with the fundamental properties of measurable functions. The Lebesgue integral is considered for both bounded functions — upper and lower integrals — and unbounded functions. Later chapters cover such topics as the Yegorov, Vitali, and Fubini theorems; convergence in measure and equi-integrability; integration and differentiation; and absolutely continuous functions. Multiple integrals and the Stieltjes integral are also examined.This book will be of interest to mathematicians and students taking pure and applied mathematics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The rating is mainly based on my desire to dig into the theory of measure and this book does the job, thoroughly and economically (both in terms of size and price).Now, Hartman’s statement about the prerequisites is somewhat optimistic : in fact, the reader should have been exposed to a full course in analysis, before approaching that subject ( e.g. Apostol’s or Goursat’s trilogies on analysis), because Hartman’s proofs are very, I mean very condensed, sometimes forcing the reader into an outguessing performance…Concerning the edition itself : highly packed text + no mention of chapter/section numbers, each 2 pages + very poor index… make the going back and forth between theorems quite painful.If you’re looking for a shorter exposition, then I suggest using Titchmarsh’s “The Theory of Functions”, chapter X, even though I personally find that book “horrific”…

⭐The rating is mainly based on my desire to dig into the theory of measure and this book does the job, thoroughly and economically (both in terms of size and price).Now, Hartman’s statement about the prerequisites is somewhat optimistic : in fact, the reader should have been exposed to a full course in analysis, before approaching that subject ( e.g. Apostol’s or Goursat’s trilogies on analysis), because Hartman’s proofs are very, I mean very condensed, sometimes forcing the reader into an outguessing performance…Concerning the edition itself : highly packed text + no mention of chapter/section numbers, each 2 pages + very poor index… make the going back and forth between theorems quite painful.If you’re looking for a shorter exposition, then I suggest using Titchmarsh’s “The Theory of Functions”, chapter X, even though I personally find that book “horrific”…

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