Real analysis: measures, integrals and applications. (English) Zbl 1279.28002

Makarov, Boris; Podkorytov, Anatolii

Universitext. London: Springer (ISBN 978-1-4471-5121-0/pbk; 978-1-4471-5122-7/ebook). xix, 772 p. (2013).

This carefully prepared textbook from Springer’s Universitext series devotes to a modern version of classical calculus. The authors base the standard theory of integration and differentiation on a more general (in fact, more simple) approach of measure theory. The presented exposition allows to more easily integrate calculus into modern analysis and it includes several attractive applications (Brun-Minkowski and Brower theorems, Khintchine and K. Ball inequalities etc.). The text is accompanied by a lot of examples and exercises.

Reviewer: Yuri A. Brudnyi (Haifa)

MSC:

28-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration
28Axx	Classical measure theory
42A16	Fourier coefficients, Fourier series of functions with special properties, special Fourier series

Keywords:

Lebesgue measure; measurable function; integral; Fourier series; Fourier transform; Radon-Nikodým theorem