Real analysis
- 1st ed.
- Oxford: Oxford University Press, 2016
- viii, 310 p.; 24 cm.
- Oxford graduate texts in mathematics .
Includes bibliographical references and index.
Real analysis is indispensable for in-depth understanding and effective application of methods of modern analysis. The core of the book describes the theory of functions of a real variable, framed in the setting of general measure and integration. Heavy emphasis is placed on measures and functions defined in Euclidean n-space; in particular, function spaces defined in terms of Lebesgue measure on Rn are treated in some detail including introduction of useful operations on these spaces, mindful that this area of real analysis plays a fundamental role in many mathematical fields and lends a helpful hand to analysis of various problems of mathematical physics and engineering. Numerous examples are included at each stage to illustrate the expressed ideas, with exercises scattered throughout the text. This book is intended primarily for graduate students, but can also be used in upper level undergraduate studies and for self-study.