Berezinian measures and graded Haar theory (Q917988)

In a previous paper the authors give an intrinsic construction of the Berezinian sheaf for a graded differentiable manifold and, using it, a more simple description of the Berezinian integral. The aim of this paper is to extend that construction to \({\mathbb{Z}}_ 2\)- graded (or super) topological spaces, and to use this to prove that for a graded topological group, the unique (up to scalar factors) Berezinian measure invariant by graded translations is the Berezinian measure associated with the ordinary Haar measure of the group.