Abstract
For a complete Boolean algebra X with measure μ, one gives conditions on the structure of the subalgebras X1 and X2 which guarantee the existence on of a strictly positive measure ν=μ1×μ2 such that the marginal measures μi are the projections of μ onto Xi.
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Literature cited
D. A. Vladimirov, Boolean Algebras [in Russian], Nauka, Moscow (1969).
D. A. Vladimirov, “On the independence of subalgebras and partitions,” J. Sov. Math.,20, No. 3 (1982).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 149, pp. 158–159, 1986.
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Samorodnitskii, A.A. Independent complements of subalgebras and product measures. J Math Sci 42, 1652–1653 (1988). https://doi.org/10.1007/BF01665054
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DOI: https://doi.org/10.1007/BF01665054