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

Abstract

The theory of sets of finite perimeter and BV functions in Wiener spaces, i.e., Banach spaces endowed with a Gaussian Borel probability measure γ, was initiated by Fukushima and Hino in [9, 10, 11], and has been further investigated in [12, 1, 2, 3]. The basic question one would like to consider is the research of infinite-dimensional analogues of the classical fine properties of BV functions and sets of finite perimeter in finite-dimensional spaces. The class of sets of finite Gaussian perimeter E in a Gaussian Banach space (X, γ) is defined by the integration by parts formula ˆ