  We call a Lebesgue-Feynman measure (LFM) any generalized measure
(distribution in the sense of Sobolev and Schwartz) on a locally convex
topological vector space E which is translation invariant. In the present
paper, we investigate transformations of the LFM generated by transformations
of the domain and also discuss the connections of these transformations of the
LFM with so-called quantum anomalies, improving some recent results of teh
authors and co-workers. We revisit the contradiction between the points of view
on quantum anomalies presented in the books of Fujikawa and Suzuki on the one
hand, and of Cartier and DeWitt-Morette on the other.
