ИСТИНА

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.