Fundamentals of Real Analysis (Paperback, Softcover reprint of the original 1st ed. 1999)

Integration theory and general topology form the core of this textbook for a first-year graduate course in real analysis. After the foundational material in the first chapter (construction of the reals, cardinal and ordinal numbers, Zorn's lemma and transfinite induction), measure, integral and topology are introduced and developed as recurrent themes of increasing depth. The treatment of integration theory is quite complete (including the convergence theorems, product measure, absolute continuity, the Radon-Nikodym theorem, and Lebesgue's theory of differentiation and primitive functions), while topology, predominantly metric, plays a supporting role. In the later chapters, integral and topology coalesce in topics such as function spaces, the Riesz representation theorem, existence theorems for an ordinary differential equation, and integral operators with continuous kernel function. In particular, the material on function spaces lays a firm foundation for the study of functional analysis.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Universitext
Release date:	March 2013
First published:	November 1998
Authors:	Sterling K. Berberian
Dimensions:	235 x 155 x 25mm (L x W x T)
Format:	Paperback
Pages:	479
Edition:	Softcover reprint of the original 1st ed. 1999
ISBN-13:	978-0-387-98480-3
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis
LSN:	0-387-98480-1
Barcode:	9780387984803

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