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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Equivalence-singularity dichotomies from zero-one laws

Authors: Raoul D. LePage and V. Mandrekar
Journal: Proc. Amer. Math. Soc. 31 (1972), 251-254
MathSciNet review: 0290442
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Abstract: In this note a general result on equivalence and singularity of two measures is presented. As a consequence of this S. Kakutani’s dichotomy for product measures and J. Feldman’s dichotomy for Gaussian measures are derived via appropriate zero-one laws.

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Keywords: Singularity, equivalence, product measure, Gaussian measure, zero-one law
Article copyright: © Copyright 1972 American Mathematical Society