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Conventional Operations on Nonstandard Constructions

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Nonstandard Analysis for the Working Mathematician

Part of the book series: Mathematics and Its Applications ((MAIA,volume 510))

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Abstract

The aim of this chapter is to illustrate how some special properties of nonstandard constructions based on conventional mathematics can be combined with ordinary mathematical methods to reveal completely new mathematical phenomena in a systematic way. The particular nonstandard construction to be exploited here is a special type of standard probability space, the Loeb space, introduced by Peter Loeb in [19]. The reader is referred to Chapter 5 of this book for this basic external object in nonstandard analysis.

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Author information

Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Yeneng Sun

Authors
  1. Yeneng Sun
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Illinois at Champaign-Urbana, Champaign-Urbana, Illinois, USA

    Peter A. Loeb

  2. Faculty of Mathematics, Universität Tübingen, Tübingen, Germany

    Manfred Wolff

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© 2000 Springer Science+Business Media Dordrecht

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Sun, Y. (2000). Conventional Operations on Nonstandard Constructions. In: Loeb, P.A., Wolff, M. (eds) Nonstandard Analysis for the Working Mathematician. Mathematics and Its Applications, vol 510. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4168-0_7

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  • DOI: https://doi.org/10.1007/978-94-011-4168-0_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6341-5

  • Online ISBN: 978-94-011-4168-0

  • eBook Packages: Springer Book Archive

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