Nonstandard Analysis for the Working Mathematician
Kluwer Academic Publishers
Published on 30. June 2000
Book
Paperback/Softback
XIV, 311 pages
978-0-7923-6341-5 (ISBN)
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Description
This book is addressed to mathematicians working in analysis and its applications. The aim is to provide an understandable introduction to the basic theory of nonstan dard analysis in Part I, and then to illuminate some of its most striking applications. Much of the book, in particular Part I, can be used in a graduate course; problems are posed in all chapters. After Part I, each chapter takes up a different field for the application of nonstandard analysis, beginning with a gentle introduction that even non-experts can read with profit. The remainder of each chapter is then addressed to experts, showing how to use nonstandard analysis in the search for solutions of open problems and how to obtain rich new structures that produce deep insight into the field under consideration. The applications discussed here are in functional analysis including operator theory, probability theory including stochastic processes, and economics including game theory and financial mathematics. In all of these areas, the intuitive notion of an infinitely small or infinitely large quantity plays an essential and helpful role in the creative process. For example, Brownian motion is often thought of as a random walk with infinitesimal increments; the spectrum of a selfadjoint operator is viewed as the set of "almost eigenvalues"; an ideal economy consists of an infinite number of agents each having an infinitesimal influence on the economy. Already at the level of calculus, one often views the integral as an infinitely large sum of infinitesimal quantities.
More details
Series
Edition
Softcover reprint of the original 1st ed. 2000
Language
English
Place of publication
Dordrecht
Netherlands
Target group
College/higher education
Professional and scholarly
Research
Product notice
Paperback (trade)
Illustrations
biography
Dimensions
Height: 24 cm
Width: 16 cm
Thickness: 17 mm
Weight
1020 gr
ISBN-13
978-0-7923-6341-5 (9780792363415)
DOI
10.1007/978-94-011-4168-0
Schweitzer Classification
Other editions
Additional editions

Peter A. Loeb | Manfred P.H. Wolff
Nonstandard Analysis for the Working Mathematician
Book
06/2000
Kluwer Academic Publishers
€117.69
Article exhausted; check for reprint
Content
Preface. I: An Introduction to Nonstandard Analysis; P.A. Loeb. 1. A Simple Introduction to Nonstandard Analysis. 2. An Introduction to General Nonstandard Analysis. 3. Topology and Measure Theory. II: Functional Analysis; M.P.H. Wolff. 4. Functional Analysis. III: Measure and Probability Theory and Applications; H. Osswald, Y. Sun. 5. Measure Theory and Integration. 6. Probability Theory. 7. Conventional Operations on Nonstandard Constructions. IV: Economics and Nonstandard Analysis; Y. Sun. 8. Nonstandard Analysis in Mathematical Economics. Index.