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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

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 | References | Similar Articles | Additional Information

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0792833-3
PII: S 0002-9947(1985)0792833-3
Article copyright: © Copyright 1985 American Mathematical Society