Blackwell, David; Maitra, Ashok Factorization of probability measures and absolutely measurable sets. (English) Zbl 0554.60001 Proc. Am. Math. Soc. 92, 251-254 (1984). The main result of the paper is as follows. Theorem. Let Y be a separable metric space. Then the following conditions on Y are equivalent. (a) Y is absolutely measurable, i.e., if \(\tilde Y\) is a metric completion of Y and \(\lambda\) is a probability measure on the Borel \(\sigma\)-field of \(\tilde Y,\) then Y is \(\lambda\)-measurable. (b) For any measurable space (X,\({\mathcal A})\) and any probability measure P on (X\(\times Y,{\mathcal A}\times {\mathcal B}(Y))\), P can be factored. (c) For any Polish space X and any probability measure P on (X\(\times Y,{\mathcal B}(X)\times {\mathcal B}(Y))\), P can be factored. Cited in 4 Documents MSC: 60A10 Probabilistic measure theory 60A05 Axioms; other general questions in probability 28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets 28A50 Integration and disintegration of measures Keywords:absolutely measurable set; prior distribution; posterior distribution; probability measure PDFBibTeX XMLCite \textit{D. Blackwell} and \textit{A. Maitra}, Proc. Am. Math. Soc. 92, 251--254 (1984; Zbl 0554.60001) Full Text: DOI References: [1] Miloslav Jiřina, Conditional probabilities on strictly separable \?-algebras, Czechoslovak Math. J. 4(79) (1954), 372 – 380 (Russian, with English summary). · Zbl 0058.11801 [2] Топология. Том 2, Транслатед фром тхе Енглиш бы М. Ја. Антоновский, Издат. ”Мир”, Мосцощ, 1969 (Руссиан). [3] E. Marczewski, On compact measures, Fund. Math. 40 (1953), 113 – 124. · Zbl 0052.04902 [4] Jan K. Pachl, Disintegration and compact measures, Math. Scand. 43 (1978/79), no. 1, 157 – 168. · Zbl 0402.28006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.