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

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Improved conditions for the distributivity of the product for σ-algebras with respect to the intersection. / Steinicke, Alexander; Rao, K.P.S. Bhaskara.
in: Mathematica Slovaca, Jahrgang 74.2024, Nr. 2, 24.05.2024, S. 331-338.

Publikationen: Beitrag in FachzeitschriftArtikelForschung(peer-reviewed)

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@article{5185c92e6c744ad3900ac54ae82c273b,
title = "Improved conditions for the distributivity of the product for σ-algebras with respect to the intersection",
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.",
keywords = "sigma-algebra, intersection of sigma-algebras, product sigma-algebras, counterexample for sigma-algebras, sigma-Algebra, intersection of sigma-Algebras, product sigma-Algebras, counterexample for sigma-algebras.",
author = "Alexander Steinicke and Rao, {K.P.S. Bhaskara}",
note = "Publisher Copyright: {\textcopyright} 2024 Mathematical Institute Slovak Academy of Sciences.",
year = "2024",
month = may,
day = "24",
doi = "10.1515/ms-2024-0025",
language = "English",
volume = "74.2024",
pages = "331--338",
journal = "Mathematica Slovaca",
issn = "0139-9918",
publisher = "VERSITA",
number = "2",

}

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TY - JOUR

T1 - Improved conditions for the distributivity of the product for σ-algebras with respect to the intersection

AU - Steinicke, Alexander

AU - Rao, K.P.S. Bhaskara

N1 - Publisher Copyright: © 2024 Mathematical Institute Slovak Academy of Sciences.

PY - 2024/5/24

Y1 - 2024/5/24

N2 - 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.

AB - 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.

KW - sigma-algebra

KW - intersection of sigma-algebras

KW - product sigma-algebras

KW - counterexample for sigma-algebras

KW - sigma-Algebra

KW - intersection of sigma-Algebras

KW - product sigma-Algebras

KW - counterexample for sigma-algebras.

UR - http://www.scopus.com/inward/record.url?scp=85194420697&partnerID=8YFLogxK

U2 - 10.1515/ms-2024-0025

DO - 10.1515/ms-2024-0025

M3 - Article

VL - 74.2024

SP - 331

EP - 338

JO - Mathematica Slovaca

JF - Mathematica Slovaca

SN - 0139-9918

IS - 2

ER -