Desintegration and perfectness of measure spaces (Q1118710)

The paper consists of two parts. In the first one the author proves that each finite measure P can be uniquely represented in the form \(P=Q_ 1+Q_ 2+Q_ 3,\) where \(Q_ 1\) is compact, \(Q_ 2\) is perfect and purely non-compact (i.e. if \(Q\ll Q_ 2\) and Q is compact then \(Q=0)\) and \(Q_ 3\) is purely non-perfect. This generalizes a result of \textit{D. Ramachandran} [Perfect measures. Part II (1979; Zbl 0523.60006)]. In the second part the author investigates relations between desintegration (with respect to countably generated \(\sigma\)-algebras) in the sense of \textit{J. K. Pachl} [Math. Scand. 43, 157-168 (1978; Zbl 0402.28006)] and of \textit{D. Ramachandran} (loc. cit.). In particular she proves that each Pachl-desintegrable with respect to countably generated \(\sigma\)-algebras probability is perfect and applies the Ramachandran- desintegration with respect to countably generated \(\sigma\)-algebras to the problem of inheritance of compactness by thick subsets.