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Nonstandard Analysis for the Working Mathematician

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Synopses & Reviews

Publisher Comments:

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 non-standard analysis and to illuminate some of its most striking applications. Problems are posed in all chapters. The opening chapter of the book presents a simplified form of the general theory that is suitable for the results of calculus and basic real analysis. The presentation is intended to facilitate the acquisition of basic skills in the subject, so that a reader who begins with no background in mathematical logic should find it relatively easy to continue. The book then proceeds with the full theory. Following Part I, each chapter takes up a different field for applications, 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 non-standard analysis in the search for solutions of open problems and how to obtain rich new structures that produce deep insights into the field under consideration. The particular applications discussed here are in functional analysis including operator theory, probability theory including stochastic processes, and economics including game theory and financial mathematics. In working through this book the reader should gain many new and helpful insights into the enterprise of mathematics. Audience: This work will be of interest to specialists whose work involves real functions, probability theory, stochastic processes, logic and foundations. Much of the book, in particular the introductory Part I, can be used in a graduate course.

Synopsis:

Addressed to mathematicians working in analysis and its applications, the aim of this book is to provide an understandable introduction to the basic theory of non-standard analysis and to illuminate some of its most striking applications.

Table of Contents

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.

Product Details

ISBN:
9780792363415
Editor:
Loeb, Peter A.
Editor:
Wolff, Manfred P. H.
Editor:
Loeb, Peter A.
Editor:
Wolff, Manfred P. H.
Author:
Wolff, Manfred P. H.
Author:
Loeb, Peter A.
Publisher:
Springer
Location:
Dordrecht
Subject:
General
Subject:
Mathematical Analysis
Subject:
Nonstandard mathematical analysis
Subject:
Functional Analysis
Subject:
Real functions
Subject:
Probability Theory and Stochastic Processes
Subject:
Mathematical Logic and Foundations
Subject:
Mathematics-Analysis General
Copyright:
Edition Description:
Softcover reprint of the original 1st ed. 2000
Series:
Mathematics and Its Applications (closed)
Series Volume:
v. 510
Publication Date:
20000630
Binding:
TRADE PAPER
Language:
English
Pages:
326
Dimensions:
240 x 160 mm 1020 gr

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Nonstandard Analysis for the Working Mathematician New Trade Paper
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Product details 326 pages Kluwer Academic Publishers - English 9780792363415 Reviews:
"Synopsis" by , Addressed to mathematicians working in analysis and its applications, the aim of this book is to provide an understandable introduction to the basic theory of non-standard analysis and to illuminate some of its most striking applications.
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