On Equivalence of Probability Measures

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 $L_2\lbrack T \rbrack$.