Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory
نویسندگان
چکیده
Let (X, 3, 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 % containing the algebra a, where the extended real-valued measure p. on % is generated by the standard part of v. If / is fl-measurable, then its standard part / is jR-measurable on X. If / and p. are finite, then the vintegral of / is infinitely close to the /¿-integral 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 ;'th event and a construction of standardsample functions for Poisson processes.
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