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Nonstandard Methods of Analysis : Mathematics and Its Applications - Anatoly G. Kusraev

Nonstandard Methods of Analysis

Mathematics and Its Applications

Hardcover Published: May 1994
ISBN: 9780792328926
Number Of Pages: 439

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Nonstandard Methods of Analysis is concerned with the main trends in this field; infinitesimal analysis and Boolean-valued analysis. The methods that have been developed in the last twenty-five years are explained in detail, and are collected in book form for the first time. Special attention is paid to general principles and fundamentals of formalisms for infinitesimals as well as to the technique of descents and ascents in a Boolean-valued universe. The book also includes various novel applications of nonstandard methods to ordered algebraic systems, vector lattices, subdifferentials, convex programming etc. that have been developed in recent years. For graduate students, postgraduates and all researchers interested in applying nonstandard methods in their work.

Excursus into the history of mathematical analysisp. 3
Naive fundamentals of infinitesimal methodsp. 13
Set-theoretic formalisms of nonstandard analysisp. 41
Monads in general topologyp. 81
Infinitesimals and subdifferentialsp. 112
Universes of setsp. 171
Boolean-valued universesp. 214
Functors of Boolean-valued analysisp. 263
Boolean-valued analysis of algebraic systemsp. 324
Boolean representations in functional analysisp. 377
Referencesp. 404
Indexp. 426
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792328926
ISBN-10: 0792328922
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 439
Published: May 1994
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 2.5
Weight (kg): 0.93