Field theory, regularization and the path integral measure

It is argued that the apparent arbitrariness of the ''anomaly'' in Fujikawa's approach should be placed into the context of the regularization of the theory not just the regularization of the anomaly. When the theory is regularized at the level of the action the consistent anomaly arises. The converse also holds, namely that if the anomaly is not consistent then the regulator employed does not, by itself, regulate the theory at the level of the action. The criterion that the regularization prescription be given at the outset is advocated, and a discussion of results of various two-dimensional models given. (orig.)