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arXiv · 1602.01293

An application of a functional inequality to quasi-invariance in infinite dimensions

Maria Gordina
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Abstract

One way to interpret smoothness of a measure in infinite dimensions is quasi-invariance of the measure under a class of transformations. Usually such settings lack a reference measure such as the Lebesgue or Haar measure, and therefore we can not use smoothness of a density with respect to such a measure. We describe how a functional inequality can be used to prove quasi-invariance results in several settings. In particular, this gives a different proof of the classical Cameron-Martin (Girsanov) theorem for an abstract Wiener space. In addition, we revisit several more geometric examples, even though the main abstract result concerns quasi-invariance of a measure under a group action on a measure space.

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Maria Gordina. 2016-02-03. An application of a functional inequality to quasi-invariance in infinite dimensions. https://arxiv.org/abs/1602.01293

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