Influence of nonstandard analysis


The influence of Abraham Robinson's theory of nonstandard analysis has been felt in a number of fields.

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.

Economics

Economists have used nonstandard analysis to model markets with large numbers of agents.

Education

The article by Michèle Artigue cited below concerns the teaching of analysis. Artigue devotes one page to "NSA and its weak impact on education", page 172. She writes:
Artigue continues specifically with reference to the calculus textbook:

Authors of books on hyperreals