Advances in Analysis, Probability and Mathematical Physics

Contributions of Nonstandard Analysis

  • Sergio A. Albeverio
  • Wilhelm A. J. Luxemburg
  • Manfred P. H. Wolff

Part of the Mathematics and Its Applications book series (MAIA, volume 314)

Table of contents

  1. Front Matter
    Pages i-x
  2. Analysis

    1. Front Matter
      Pages 1-1
    2. S. Albeverio, D. Guido, A. Ponosov, S. Scarlatti
      Pages 3-19
    3. M. Capiński, N. J. Cutland
      Pages 20-36
    4. Tommy Norberg
      Pages 46-55
    5. Michael Oberguggenberger
      Pages 56-74
    6. Hermann Render
      Pages 96-106
    7. G. Beate Zimmer
      Pages 132-139
  3. Probability Theory

  4. Mathematical Physics

  5. Back Matter
    Pages 247-251

About this book


In 1961 Robinson introduced an entirely new version of the theory of infinitesimals, which he called `Nonstandard analysis'. `Nonstandard' here refers to the nature of new fields of numbers as defined by nonstandard models of the first-order theory of the reals. This system of numbers was closely related to the ring of Schmieden and Laugwitz, developed independently a few years earlier.
During the last thirty years the use of nonstandard models in mathematics has taken its rightful place among the various methods employed by mathematicians. The contributions in this volume have been selected to present a panoramic view of the various directions in which nonstandard analysis is advancing, thus serving as a source of inspiration for future research.
Papers have been grouped in sections dealing with analysis, topology and topological groups; probability theory; and mathematical physics.
This volume can be used as a complementary text to courses in nonstandard analysis, and will be of interest to graduate students and researchers in both pure and applied mathematics and physics.


Probability theory Variance calculus differential equation mathematical physics

Editors and affiliations

  • Sergio A. Albeverio
    • 1
  • Wilhelm A. J. Luxemburg
    • 2
  • Manfred P. H. Wolff
    • 3
  1. 1.Faculty of MathematicsRuhr-Universität BochumBochumGermany
  2. 2.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA
  3. 3.Mathematical InstituteUniversity of TübingenTübingenGermany

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 1995
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4481-5
  • Online ISBN 978-94-015-8451-7
  • Buy this book on publisher's site
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