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Title: Sets of finite perimeter and the Hausdorff-Gauss measure on the Wiener space
Authors: Hino, Masanori  kyouindb  KAKEN_id
Author's alias: 日野, 正訓
Keywords: Geometric measure theory
Hausdorff-Gauss measure
Set of finite perimeter
Wiener space
Issue Date: 1-Mar-2010
Publisher: Elsevier Science B.V. Amsterdam
Journal title: Journal of Functional Analysis
Volume: 258
Issue: 5
Start page: 1656
End page: 1681
Abstract: In Euclidean space, the integration by parts formula for a set of finite perimeter is expressed by the integration with respect to a type of surface measure. According to geometric measure theory, this surface measure is realized by the one-codimensional Hausdorff measure restricted on the reduced boundary and/or the measure-theoretic boundary, which may be strictly smaller than the topological boundary. In this paper, we discuss the counterpart of this measure in the abstract Wiener space, which is a typical infinite-dimensional space. We introduce the concept of the measure-theoretic boundary in the Wiener space and provide the integration by parts formula for sets of finite perimeter. The formula is presented in terms of the integration with respect to the one-codimensional Hausdorff-Gauss measure restricted on the measure-theoretic boundary.
Rights: c 2009 Elsevier Inc. All rights reserved.
This is not the published version. Please cite only the published version.
DOI(Published Version): 10.1016/j.jfa.2009.06.033
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