Abstract
Feynman's work on quantum electrodynamics along with his earlier work on path integration led him to a method for forming functions of noncommuting operators. He regarded the resulting operational calculus as a generalized path integral. A new mathematically rigorous approach to Feynman's operational calculi has been initiated recently. Each of the n operators involved has associated with it a measure on an appropriate time interval, and the resulting n-vector of measures determines a particular operational calculus. The work so far has been restricted to cases where only continuous measures were used. Here we begin the study of a broader theory which includes a variety of blends of discrete and continuous measures. This extended theory brings us into direct contact with much earlier work on Feynman's operational calculus and, in addition, gives rise to many natural questions