Modern real analysis / William P. Ziemer ; with contributions by Monica Torres

This book provides an accessible self-contained introduction to modern real analysis suitable for graduate students with an understanding of advanced calculus. It may also provide a useful reference for more experienced mathematicians. The focus of the book is on measure and integration, which are nicely connected to closely related topics such as bounded variation and absolutely continuous functions, representation theorems for linear functionals, Sobolev spaces and distributions. Topics such as Hausdorff measure and dimension, the Marcinkiewicz interpolation theorem, differentiation of measures and connections to functional analysis, which sometimes do not appear in similar books, are fully treated. The topics are nicely brought together at the end with an application to the Dirichlet problem for Laplace's equation.
A particular strength of the book is its well chosen material, virtually all of which is important for those working in real analysis to be aware of. The book is also accessible and self-contained with short chapters on set theory, topology and functional analysis which recall the necessary background. The different topics are clearly related with helpful discussion and examples given as motivation throughout. There are also many exercises at the end of each subsection. ... (MSN)

Bibliogr. p. 375-377. Index