The Gauss–Green theorem in stratified groups

We lay the foundations for a theory of divergence-measure fields in noncommutative stratified nilpotent Lie groups. Such vector fields form a new family of function spaces, which generalize in a sense the BV fields. They provide the most general setting to establish Gauss–Green formulas for vector fields of low regularity on sets of finite perimeter. We show several properties of divergence-measure fields in stratified groups, ultimately achieving the related Gauss–Green theorem.