A quasi-invariance theorem for measures on Banach spaces

Bell, Denis

doi:10.1090/S0002-9947-1985-0792833-3

A quasi-invariance theorem for measures on Banach spaces
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Trans. Amer. Math. Soc. 290 (1985), 851-855 Request permission

Abstract:

We show that for a measure $\gamma$ on a Banach space directional differentiability implies quasi-translation invariance. This result is shown to imply the Cameron-Martin theorem. A second application is given in which $\gamma$ is the image of a Gaussian measure under a suitably regular map.

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