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On the extremality of regular extensions of contents and measures

Wolfgang Adamski — 1995

Commentationes Mathematicae Universitatis Carolinae

Let 𝒜 be an algebra and 𝒦 a lattice of subsets of a set X . We show that every content on 𝒜 that can be approximated by 𝒦 in the sense of Marczewski has an extremal extension to a 𝒦 -regular content on the algebra generated by 𝒜 and 𝒦 . Under an additional assumption, we can also prove the existence of extremal regular measure extensions.

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