Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sets of finite perimeter and the Hausdorff-Gauss measure on the Wiener
  space   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.

18
The categories of this paper are: econ
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph