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Nonstandard Methods of Analysis

  • Book
  • © 1994

Overview

Authors:
  1. Anatoly G. Kusraev

    1. Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia

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  2. Semen S. Kutateladze

    1. Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-viii
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  2. Infinitesimal Analysis

    1. Front Matter

      Pages 1-2
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    2. Excursus into the History of Mathematical Analysis

      • Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 3-12

    3. Naive Fundamentals of Infinitesimal Methods

      • Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 13-40

    4. Set-Theoretic Formalisms of Nonstandard Analysis

      • Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 41-80

    5. Monads in General Topology

      • Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 81-111

    6. Infinitesimals and Subdifferentials

      • Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 112-168

  3. Boolean-Valued Analysis

    1. Front Matter

      Pages 169-171
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    2. Universes of Sets

      • Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 171-213

    3. Boolean-Valued Universes

      • Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 214-262

    4. Functors of Boolean-Valued Analysis

      • Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 263-323

    5. Boolean-Valued Analysis of Algebraic Systems

      • Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 324-376

    6. Boolean Representations in Functional Analysis

      • Anatoly G. Kusraev, Semen S. Kutateladze
      Pages 377-403

  4. Back Matter

    Pages 404-439
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Keywords

About this book

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.

Authors and Affiliations

  • Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia

    Anatoly G. Kusraev, Semen S. Kutateladze

Bibliographic Information

  • Book Title: Nonstandard Methods of Analysis

  • Authors: Anatoly G. Kusraev, Semen S. Kutateladze

  • Series Title: Mathematics and Its Applications

  • DOI: https://doi.org/10.1007/978-94-011-1136-2

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1994

  • Hardcover ISBN: 978-0-7923-2892-6Published: 31 May 1994

  • Softcover ISBN: 978-94-010-4497-4Published: 20 October 2012

  • eBook ISBN: 978-94-011-1136-2Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: VIII, 439

  • Additional Information: Originally published in Russian

  • Topics: Mathematical Logic and Foundations, Real Functions, Functional Analysis, Topology, Optimization

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