Ziemer W.P. Modern Real Analysis

2nd Edition. — Springer International Publishing AG, 2017. — 444 p. — (Graduate Texts in Mathematics 278) — ISBN: 978-3-319-64628-2.This text is an essentially self-contained treatment of material that is normally found in a first-year graduate course in real analysis. Although the presentation is based on a modern treatment of measure and integration, it has not lost sight of the fact that the theory of functions of one real variable is the core of the subject. It is assumed that the student has had a solid course in Advanced Calculus. Although the book’s primary purpose is to serve as a graduate text, we hope that it will also serve as useful reference for the more experienced mathematician.Preliminaries
Real, Cardinal, and Ordinal Numbers
Elements of Topology
Measure Theory
Measurable Functions
Integration
Differentiation
Elements of Functional Analysis
Measures and Linear Functionals
Distributions
Functions of Several Variables