Improved conditions for the distributivity of the product for σ-algebras with respect to the intersection
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In: Mathematica Slovaca, Vol. 74.2024, No. 2, 24.05.2024, p. 331-338.
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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 -
