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URLﾘﾝｸ(en.wikipedia.org)
Peter A. Loeb
Peter Albert Loeb is a mathematician at the University of Illinois at Urbana–Champaign. He co-authored a basic reference text on nonstandard analysis (Hurd–Loeb 1985). Reviewer Perry Smith for MathSciNet wrote:
This book is a welcome addition to the literature on nonstandard analysis.[1]
The notion of Loeb measure named after him has become a standard tool in the field.[2]
In 2012 he became a fellow of the American Mathematical Society.[3]
See also
Influence of nonstandard analysis
URLﾘﾝｸ(en.wikipedia.org)
Influence of nonstandard analysis
The influence of Abraham Robinson's theory of nonstandard analysis has been felt in a number of fields.
Contents
1 Probability theory
2 Economics
3 Education
4 Authors of books on hyperreals
Probability theory
"Radically elementary probability theory" of Edward Nelson combines the discrete and the continuous theory through the infinitesimal approach. The model-theoretical approach of nonstandard analysis together with Loeb measure theory allows one to define Brownian motion as a hyperfinite random walk, obviating the need for cumbersome measure-theoretic developments. Jerome Keisler used this classical approach of nonstandard analysis to characterize general stochastic processes as hyperfinite ones.