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

Abstract: We study properties of functions with bounded variation in Carnot-Ca-ra-th\'eo-do-ry 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 $\mathcal R$, we show that almost all approximate discontinuities are of jump type and we study a representation formula for the jump part of the derivative.