Towards a theory of BV functions in abstract Wiener spaces

Functions of bounded variation in an abstract Wiener space, i.e., an infinite dimensional Banach space endowed with a Gaussian measure and a related differentiable structure, have been introduced by M. Fukushima and M. Hino using Dirichlet forms, and their properties have been studied with tools from stochastics. In this paper we reformulate, with purely analytical tools, the definition and the main properties of BV functions, and start investigating further properties.