Exceptional families of measures on Carnot groups

We study the families of measures on Carnot groups that have vanishing $p$-module, which we call $p$-exceptional families. We found necessary and sufficient condition for the family of intrinsic Lipschitz surfaces passing through a common point to be $p$-exceptional for $p\ge 1$. We described a wide class of $p$-exceptional intrinsic Lipschitz surfaces for $p\in (0,\mathrm{\infty })$.