Principles of real analysis: measure, integration, functional analysis, and applications

The aim of this text is to prepare the reader for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. The book is also suitable as a means to prepare for qualifying exams in real analysis. It is designed so that the reader or instructor may be selective in choosing topics to suit a variety of needs. The text includes a wide variety of detailed topics and it is hoped that the text will be seen as both a valuable reference and as an efficient and streamlined excursion through advanced real analysis. "Scenic routes" are many and, I hope, enticing, but they are optional and plainly marked.