Abstract
1. Fundamental concepts. With the establishment of the consistency of the conditions determining collectives,: we obtain a sound basis for the theory of probability. We shall see that certain slight modifications of these conditions will be necessary in order to establish consistency but these modifications will destroy none of the intrinsic value of von Mises' theory. In those alternative systems for which consistency has been established, the conditions are so much weaker than those of von Mises that much of the value of his theory has been lost. The collective is a mathematical idealization of a sequence of occurrences (measurements, tosses of a coin, etc.). A collective K consists of an infinite sequence of elements (points of some space S). Thus?
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