[en] In this paper we show that the variation of the integral measure is fully equivalent to the authentic field theoretical treatment for a two-point function. To do this we first examine various ways of solving the factor A(x) in Fujikawa's expression for the functional integral measure. We define the anomaly as A(x)-A_f (x), where A_f(x) is the Fujikawa factor for the free field. We then propose a regulator which leads to a finite result for any anomaly. We then show that the A(x) can be defined in terms of the proper-time through a splitting procedure. The original Fujikawa prescription for A(x) is shown to be closely related to the proper-time description of the anomaly, initiated by Schwinger. Its equivalence to the authentic field theoretical treatment will be proven as a consequence of these investigations. The ξ-functional regularization for A(x) is also examined. Then we will examine the way to deduce the anomaly from the effective potential by adopting the Φ⁴ model as an example. The renormalization group equation for the effective potential is solved exactly to obtain the precise form of the β-function in terms of which we reexpress the result obtained in a previous section for A(x). We discuss the physical significance of the renormalization group equation for the case of broken symmetry