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August, 1973 On Equivalence of Probability Measures
Charles R. Baker
Ann. Probab. 1(4): 690-698 (August, 1973). DOI: 10.1214/aop/1176996895

Abstract

Let $H$ be a real and separable Hilbert space, $\Gamma$ the Borel $\sigma$-field of $H$ sets, and $\mu_1$ and $\mu_2$ two probability measures on $(H, \Gamma)$. Several sufficient conditions for equivalence (mutual absolute continuity) of $\mu_1$ and $\mu_2$ are obtained in this paper. Some of these results do not require that $\mu_1$ and $\mu_2$ be Gaussian. The conditions obtained are applied to show equivalence for some specific measures when $H$ is $L_2\lbrack T \rbrack$.

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Charles R. Baker. "On Equivalence of Probability Measures." Ann. Probab. 1 (4) 690 - 698, August, 1973. https://doi.org/10.1214/aop/1176996895

Information

Published: August, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0295.60002
MathSciNet: MR368126
Digital Object Identifier: 10.1214/aop/1176996895

Keywords: Absolute continuity , Gaussian measures , Measures on Hilbert space

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 4 • August, 1973
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