Exceptional families of measures on Carnot groups

Abstract

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

Keywords

• nilpotent lie group
• module of families of measures
• hausdorff measure
• intrinsic lipschitz graph
• primary 28a78
• 53c17
• secondary 31b15
• 22e30