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In recent years probability theory has been formulated mathematically as measure theory; in the case of stochastic processes depending upon a continuous parameter the measures considered are defined on certain subspaces of the space of all functions of a real variable.! This formulation of stochastic processes depending upon a continuous parameter gives rise to certain measurability problems, and it is with these measurability problems that this paper is concerned. In particular we shall bedoi:10.1090/s0002-9947-1940-0000918-4 fatcat:kd26fdt5kjb6rpp6lx2x2tqfi4