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Let (X, (!, v) be an internal measure space in a denumerably comprehensive enlargement. The set X is a standard measure space when equipped with the smallest standard o'algebra Xi containing the algebra d, where the extended real-valued measure ja on XR is generated by the standard part of v. If f is d-measurable, then its standard part Of is JR-measurable on X. If f and p, are finite, then the -integral of f is infinitely close to the a-integral of Of. Applications include coin tossing and Poisson processes. In particular, there is an elementary proof of the strong Markov property for the stopping time of the jth event and a construction of standard sample functions for Poisson processes.

Conversion from nonstandard to standard measure spaces and applications in probability theory