On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces

TL;DR

This paper investigates sets of finite perimeter in Wiener spaces and demonstrates that at almost every point, these sets locally resemble halfspaces when scaled up, revealing their geometric structure.

Contribution

It establishes the blow-up behavior of finite perimeter sets in Wiener spaces, showing convergence to halfspaces at almost every boundary point.

Findings

Finite perimeter sets in Wiener spaces blow-up to halfspaces at almost every boundary point.

The result extends geometric measure theory to infinite-dimensional Wiener spaces.

Provides a foundation for understanding the local structure of sets in stochastic analysis.

Abstract

We study sets of finite perimeter in Wiener space, and prove that at almost every point (with respect to the perimeter measure) a set of finite perimeter blows-up to a halfspace.