Abraham Robinson's theory of nonstandard analysis has been applied in a number of fields.
"Radically elementary probability theory" of Edward Nelson combines the discrete and the continuous theory through the infinitesimal approach.[citation needed][1] 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.[citation needed][2] Jerome Keisler used this classical approach of nonstandard analysis to characterize general stochastic processes as hyperfinite ones.[citation needed][3]
Economists have used nonstandard analysis to model markets with large numbers of agents (see Robert M. Anderson (economist)).
An article by Michèle Artigue[4] concerns the teaching of analysis. Artigue devotes a section, "The non standard analysis and its weak impact on education" on page 172, to non-standard analysis. She writes:
Artigue continues specifically with reference to the calculus textbook:
{{cite book}}
: CS1 maint: location missing publisher (link)