Inserted: 5 feb 2002
Last Updated: 28 jan 2004
Journal: Math. Z.
We prove the almost everywhere approximate differentiability of functions with bounded variation in stratified groups and we study their approximate discontinuity set. We introduce functions of bounded higher order variation and obtain a weak version of Alexandroff differentiability theorem in this context. We present a nontrivial class of functions with second order bounded variation, arising from inf-convolution formula of a suitable ``cost'' function.
Keywords: BV functions, stratified groups, differentiability