突然ですが、メモ貼る（＾＾ https://en.wikipedia.org/wiki/Peter_A._Loeb 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
https://en.wikipedia.org/wiki/Influence_of_nonstandard_analysis 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.
