Improved conditions for the distributivity of the product for σ-algebras with respect to the intersection
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- Indiana University Northwest
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.
Details
Original language | English |
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Pages (from-to) | 331-338 |
Number of pages | 8 |
Journal | Mathematica Slovaca |
Volume | 74.2024 |
Issue number | 2 |
DOIs | |
Publication status | Published - 24 May 2024 |