Improved conditions for the distributivity of the product for σ-algebras with respect to the intersection

Alexander Steinicke, K.P.S. Bhaskara Rao

Publikation: Beitrag in FachzeitschriftArtikelForschungBegutachtung

Abstract

We present a variety of refined conditions for σ-Algebras A (on a set X), F; G (on a set U) such that the distributivity equation (Formula Presented) The article generalizes the results in an article of Steinicke (2021) and includes a positive result for-Algebras generated by at most countable partitions, which was not covered before. We also present a proof that counterexamples may be constructed whenever X is uncountable and there exist two α-Algebras on X which are both countably separated, but their intersection is not. We present examples of such structures. In the last section, we extend Theorem 2 in Steinicke (2021) from analytic to the setting of Blackwell spaces.

OriginalspracheEnglisch
Seiten (von - bis)331-338
Seitenumfang8
FachzeitschriftMathematica Slovaca
Jahrgang74.2024
Ausgabenummer2
DOIs
PublikationsstatusVeröffentlicht - 24 Mai 2024

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