Measures and Integrals in Conditional Set Theory
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In particular, this extends the usual representation results for separable spaces.
KeywordsConditional set theory Conditional measure theory Vector-valued measure Kernel Conditional distribution
Mathematics Subject Classification (2010)03C90 28B15 46G10 60Axx
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A.J. and M.K. gratefully acknowledge financial support from DFG project KU 2740/2-1. The authors would like to thank an anonymous referee for a careful reading of the manuscript and helpful comments and suggestions.
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