On the extremality of regular extensions of contents and measures. (English) Zbl 0834.28001

Adamski, Wolfgang

Commentat. Math. Univ. Carol. 36, No. 2, 213-218 (1995).

From author’s summary” “Let \({\mathcal A}\) be an algebra and \({\mathcal K}\) a lattice of subsets of a set \(X\). We show that every content on \({\mathcal A}\) that can be approximated by \({\mathcal K}\) in the sense of Marczewski has an extremal extension to a \({\mathcal K}\)-regular content on the algebra generated by \({\mathcal A}\) and \({\mathcal K}\). Under an additional assumption, we can also prove the existence of extremal regular measure extensions”.

Reviewer: D.Plachky (Münster)

MSC:

28A12

Contents, measures, outer measures, capacities

Keywords:

regular content; semicompact; sequentially dominated; lattice; extremal regular measure extensions