Skip to main content
SpringerLink
Log in
Book cover
  • Book
  • © 1994

Nonstandard Methods of Analysis

Authors:

  1. Anatoly G. Kusraev

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

    View author publications

    You can also search for this author in PubMed   Google Scholar

  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)

Sections

Buy it now

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (10 chapters)

  1. Front Matter

    Pages i-viii
    PDF

  2. Infinitesimal Analysis

    1. Front Matter

      Pages 1-2
      PDF

    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
      PDF

    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
    PDF
Back to top

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.
Back to top

Keywords

Back to top

Authors and Affiliations

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

    Anatoly G. Kusraev, Semen S. Kutateladze

Back to top

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

Back to top

Publish with us

Policies and ethics

Back to top
Access via your institution

Buy it now

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Search

Navigation