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X: 30, 545-577, LNM 511 (1976)
DELLACHERIE, Claude
Sur la construction de noyaux boréliens (Measure theory)
This answers questions of Getoor 923 and Meyer 924 on the regularization of a pseudo-kernel relative to a family ${\cal N}$ of negligible sets into a Borel kernel. The problem is reduced to a simpler one, whether a non-negligible set $A$ contains a non-negligible Borel set, which itself is answered in the affirmative if 1) The underlying space is compact metric, 2) $A$ is coanalytic, 3) ${\cal N}$ consists of all sets negligible for all measures of an analytic family. The proof uses general methods, of independent interest
Comment: For a presentation in book form, see Dellacherie-Meyer, Probabilités et Potentiel C, chapter XI 41. The hypothesis that the space is compact is sometimes troublesome for the applications
Keywords: Pseudo-kernels, Regularization
Nature: Original
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