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

Alexander Steinicke

doi:10.1007/s00013-020-01571-z

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

Alexander Steinicke

Lehrstuhl für Angewandte Mathematik (170)

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Begutachtung

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.

Originalsprache	Englisch
Seiten (von - bis)	667-675
Seitenumfang	9
Fachzeitschrift	Archiv der Mathematik
Jahrgang	116
Ausgabenummer	6
DOIs	https://doi.org/10.1007/s00013-020-01571-z
Publikationsstatus	Veröffentlicht - Juni 2021

Bibliographische Notiz

Funding Information:
The author wants to thank Karin Schnass, University of Innsbruck, and Gunther Leobacher, University of Graz, for fruitful discussions and valuable suggestions.

Publisher Copyright:
© 2021, The Author(s).

Zugriff auf Dokument

10.1007/s00013-020-01571-z

https://arxiv.org/abs/2007.06095

Andere Dateien und Links

Link to publication in Scopus

Dieses zitieren

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