The focus of this modern graduate text in real analysis is to prepare the potential researcher to a rigorous "way of thinking" in applied mathematics and partial differential equations. The book will provide excellent foundations and serve as a solid building block for research in approximation theory and probability, analysis, PDEs, and the calculus of variations. May be used in an introductory graduate course in analysis and measure theory, or as a preparatory text by anyone expecting to work in analysis, PDEs, and applied mathematics.

This graduate text in real analysis is a solid building block for research in analysis, PDEs, the calculus of variations, probability, and approximation theory. It covers all the core topics, such as a basic introduction to functional analysis, and it discusses other topics often not addressed including Radon measures, the Besicovitch covering Theorem, the Rademacher theorem, and a constructive presentation of the Stone-Weierstrass Theoroem.

Preface * Preliminaries * Topologies and Metric Spaces * Measuring Sets * The Lebesgue Integral * Topics on Measurable Functions of Real Variables * The L^p Spaces * Banach Spaces * Spaces of Continuous Functions, Distributions, and Weak Derivitives * Topics on Integrable Functions of Real Variables * Embedding of W ^1,p (E) into L^q (E) * References * Index