Hausdorff measures on the Wiener space. (English) Zbl 1081.28500

Feyel, D.; de La Pradelle, A.

Potential Anal. 1, No. 2, 177-189 (1992).

Summary: We construct a Hausdorff measure of finite co-dimension on the Wiener space. We then extend the Federer co-area formula to this Wiener space for functions with the sole condition that they belong to the first Sobolev space. An explicit formula for the density of the images of the Wiener measure under such functions follows naturally from this. As a corollary, this yields a new and easy proof of the Krée-Watanabe theorem concerning the regularity of the images of the Wiener measure.

MSC:

28A75	Length, area, volume, other geometric measure theory
28C20	Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
46G12	Measures and integration on abstract linear spaces
60H07	Stochastic calculus of variations and the Malliavin calculus

Keywords:

Hausdorff measures; Wiener measures; Gaussian measures; Sobolev spaces; Malliavin calculus

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