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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
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Kolmogorov doesn't show existence of Dirichlet process for arbitrary measurable spaces. Why?
Constructing the Dirichlet process using Kolmogorov raises several problems, and your question shows that you are already on to some of them. In short, an arbitrary measurable space is not sufficient, …