Influence of nonstandard analysis
Abraham Robinson's theory of nonstandard analysis has been applied 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
An article by Michèle Artigue 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:
Authors of books on hyperreals
- Sergio Albeverio
- Robert M. Anderson (economist)
- Leif Arkeryd
- Vieri Benci
- Nigel Cutland
- Martin Davis
- Jens Erik Fenstad
- Robert Goldblatt
- Reuben Hersh
- Raphael Høegh-Krohn
- Karel Hrbáček
- Vladimir Kanovei
- H. Jerome Keisler
- Semen Samsonovich Kutateladze
- Peter Loeb
- Wilhelmus Luxemburg
- Edward Nelson
- Alain M. Robert
- Abraham Robinson
- Keith Stroyan
- Terence Tao