Zero-One Laws for Gaussian Measures on Banach Space
Zero-One Laws for Gaussian Measures on Banach Space
Let $\mathcal {B}$ be a real separable Banach space, $\mu$ a Gaussian measure on the Borel $\sigma$-field of $\mathcal {B}$, and ${B_\mu }[\mathcal {B}]$ the completion of the Borel $\sigma$-field under $\mu$. If $G \in {B_\mu }[\mathcal {B}]$ is a subgroup, we show that $\mu (G) = 0$ or 1, …