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Topology and Measure Theory

  • Peter A. Loeb
Chapter
  • 407 Downloads
Part of the Mathematics and Its Applications book series (MAIA, volume 510)

Abstract

We begin this chapter by showing that nonstandard analysis simplifies many of the ideas in the study of metric and topological spaces. Most of the initial results on topology can be found in Robinson’s book [30]. We then give some recent applications of nonstandard analysis to topology. The chapter concludes with a quick introduction to the applications of nonstandard analysis in measure and probability theory. For this purpose, we assume the reader is familiar with the Carathéodory Extension Theorem. A full introduction to this rich theory, starting from first principles, is given in Horst Osswald’s chapters in Part III of this book.

Keywords

Topological Space Measure Theory Countable Base Nonstandard Analysis Base Generate Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Peter A. Loeb
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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