Research Catalog

Nonstandard methods of analysis

Title
Nonstandard methods of analysis / by Anatoly G. Kusraev and Semen S. Kutateladze.
Author
Kusraev, A. G.
Publication
Dordrecht ; Boston : Kluwer Academic Publishers, [1994], ©1994.

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Details

Additional Authors
Kutateladze, S. S. (Semen Samsonovich)
Description
viii, 435 pages : illustrations; 25 cm.
Summary
  • This volume is devoted to nonstandard methods of analysis based on applying nonstandard models of set theory. The present monograph is concerned with the main trends in this field, infinitesimal analysis and Boolean-valued analysis. Here, the methods that have been developed in the last twenty-five years are explained in detail, and are collected in bookform 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 were developed in recent years.
Series Statement
Mathematics and its applications ; v. 291
Uniform Title
  • Nestandartnye metody analiza. English
  • Mathematics and its applications (Kluwer Academic Publishers) ; v. 291.
Alternative Title
Nestandartnye metody analiza.
Subject
Bibliography (note)
  • Includes bibliographical references (p. 404-425) and index.
Contents
Excursus into the history of mathematical analysis -- Naive fundamentals of infinitesimal methods -- Set-theoretic formalisms of nonstandard analysis -- Monads in general topology -- Infinitesimals and subdifferentials -- Universes of sets -- Boolean-valued universes -- Functors of Boolean-valued analysis -- Boolean-valued analysis of algebraic systems -- Boolean representations in functional analysis.
ISBN
0792328922 (acid-free paper)
LCCN
94016567
OCLC
  • 30438667
  • ocm30438667
Owning Institutions
Columbia University Libraries