Аннотация:We discuss the problem concerning the origin of quantum anomalies which has
been the source of disagreement in the literature. Our approach is based on
the differential properties of families of generalized measures. To this end, we
introduce a space of test functions over a locally convex topological vector space,
and define the concept of logarithmic derivatives of corresponding generalized
measures. In particular, we show that quantum anomalies are readily understood
in terms of the differential properties of the Lebesgue-Feynman generalized
measures (equivalently, of the Feyman path integrals). We formulate a precise
definition for quantum anomalies in these terms.