Analysis: Foundations and Applications

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.