Exceptional families of measures on Carnot groups

Abstract

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