Fine properties of functions with bounded variation in Carnot-Carathéodory spaces

Abstract

We study properties of functions with bounded variation in Carnot-Carathéodory spaces. We prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of their distributional derivatives. Under an additional assumption on the space, called property R, we show that almost all approximate discontinuities are of jump type and we study a representation formula for the jump part of the derivative.