Purification of measure-valued maps. (English) Zbl 1107.28007
The authors study the purification of measure-valued maps. In the main theorem they study measurable mappings from a nonatomic Loeb probability space to the space of Borel probability measures on a compact metric space. They show that for a measurable mapping \(f\) between the spaces one can find a measurable mapping \(g\) between the spaces such that \(f\) and \(g\) yield the same values for the integrals associated with a countable class of functions between the spaces. As corollaries they obtain results that generalize the classical Dvoretzky-Wald-Wolfwitz theorem. They also deduce certain other interesting and useful results.
Reviewer: Ganesh Datta Dikshit (Auckland)
MSC:
28A25 | Integration with respect to measures and other set functions |
28E05 | Nonstandard measure theory |
03H05 | Nonstandard models in mathematics |
91A06 | \(n\)-person games, \(n>2\) |
26E35 | Nonstandard analysis |