Topology and Measure Theory

Peter A. Loeb ()
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Peter A. Loeb: University of Illinois, Department of Mathematics

Chapter Chapter 3 in Nonstandard Analysis for the Working Mathematician, 2015, pp 79-104 from Springer

Abstract: Abstract We begin this chapter by showing that nonstandard analysis simplifies many of the ideas in the study of metric and topological spaces. After some introductory material, we will present a few more 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.

Keywords: Nonstandard Analysis; Nonstandard Extension; Neighborhood Filter Base; Internal Probability Measure; Riemann Integration Theory (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-7327-0_3

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DOI: 10.1007/978-94-017-7327-0_3

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