Derivatives of generalized measures and quantum anomalies

One sais that a quantum anomaly occurs if after a quantization of a classical Lagrangian (or Hamiltonian) system, whos action is invariant with respect to a transformation, one get a quantum system which is no longer invariant with respect to the transformation. Relatively resently the following two books were published: "Path Integrals and Quantum Anomalies" (Oxford Univ. Press, 2004) by K. Fujikawa and H. Suzuki, and "Functional Integration: Action and Symmetries" (Cambridge Univ. Press, 2007) by P. Cartier and C. DeWitt-Morette. The explanations of the quantum anomalies given in these books contradict to each other. In the talk one suggest a new method of describing of origin of this phenomenon based on using the logarithmic derivatives of generalized measures. The obtained results imply that the point of view of Fujikawa and Suzuki is correct.