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Nonstandard Methods of Analysis

  • Anatoly G. Kusraev
  • Semen S. Kutateladze
Book

Part of the Mathematics and Its Applications book series (MAIA, volume 291)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Infinitesimal Analysis

    1. Front Matter
      Pages 1-2
    2. Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 3-12
    3. Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 13-40
    4. Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 41-80
    5. Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 81-111
    6. Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 112-168
  3. Boolean-Valued Analysis

    1. Front Matter
      Pages 169-171
    2. Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 171-213
    3. Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 214-262
    4. Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 263-323
    5. Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 324-376
    6. Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 377-403
  4. Back Matter
    Pages 404-439

About this book

Introduction

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.

Keywords

Mathematica functional analysis mathematical analysis topology

Authors and affiliations

  • Anatoly G. Kusraev
    • 1
  • Semen S. Kutateladze
    • 1
  1. 1.Institute of MathematicsRussian Academy of SciencesNovosibirskRussia

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