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Transactions of the American Mathematical Society

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A quasi-invariance theorem for measures on Banach spaces

Author: Denis Bell
Journal: Trans. Amer. Math. Soc. 290 (1985), 851-855
MSC: Primary 46G12; Secondary 28C20
MathSciNet review: 792833
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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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Article copyright: © Copyright 1985 American Mathematical Society