(Non-)Distributivity of the Product for σ-Algebras with Respect to the Intersection

Publikationen: Beitrag in FachzeitschriftArtikelForschung(peer-reviewed)

Abstract

We study the validity of the distributivity equation (A⊗F)∩(A⊗G)=A⊗(F∩G),where A is a σ-algebra on a set X, and F, G are σ-algebras on a set U. We present a counterexample for the general case and in the case of countably generated subspaces of analytic measurable spaces, we give an equivalent condition in terms of the σ-algebras’ atoms. Using this, we give a sufficient condition under which distributivity holds.

Details

OriginalspracheEnglisch
Seiten (von - bis)667-675
Seitenumfang9
FachzeitschriftArchiv der Mathematik
Jahrgang116
Ausgabenummer6
DOIs
StatusVeröffentlicht - Juni 2021