Berezin integration on DeWitt supermanifolds (Q1802781)

The author shows that Berezin integration can be consistently defined on a supermanifold of DeWitt type based on a graded-commutative Banach algebra. The integral is a real-valued functional on the space of compactly supported global sections of the Berezinian sheaf of the supermanifold. DeWitt supermanifolds have more morphisms than graded supermanifolds. So the Berezin integral over a DeWitt supermanifold is invariant under the full group of diffeomorphisms of this supermanifold.