Nonstandard Methods of Analysis

By: A.G. Kusraev, SemÃ«n Samsonovich Kutateladze

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Hardcover | 1 May 1994

At a Glance

Hardcover
452 Pages

Dimensions(cm)
23.39 x 15.6 x 2.54

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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.

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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Mathematical Logic Geometry Optimisation Linear Programming Topology Calculus & Mathematical Analysis Functional Analysis & Transforms Applied Mathematics

Introduction
Excursus into the history of mathematical analysis	p. 3
Naive fundamentals of infinitesimal methods	p. 13
Set-theoretic formalisms of nonstandard analysis	p. 41
Monads in general topology	p. 81
Infinitesimals and subdifferentials	p. 112
Universes of sets	p. 171
Boolean-valued universes	p. 214
Functors of Boolean-valued analysis	p. 263
Boolean-valued analysis of algebraic systems	p. 324
Boolean representations in functional analysis	p. 377
References	p. 404
Index	p. 426
Table of Contents provided by Blackwell. All Rights Reserved.

Nonstandard Methods of Analysis

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Hardcover

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