Exceptional families of measures on Carnot groups

Abstract

We study the families of measures on Carnot groups that have vanishing p -module, which we call Mp -exceptional families. We found necessary and sufficient Conditions for the family of intrinsic Lipschitz surfaces passing through a common point to be Mp -exceptional for p≥1 . We describe a wide class of Mp -exceptional intrinsic Lipschitz surfaces for p∈(0,∞) .