Abstract
H. D. Block and J. Marschak have presented in the Bulletin of the American Mathematical Society vol. 65 (1959) pp. 123-124, an identity which arose in a probability context. This note proves it by a probability theoretical argument. Consider an experiment having the set of possible outcomes N--{ 1, I. ., n} with positive probabilities (ui, * * *, u) and an infinite sequence of independent repetitions of that experiment. Let M be a subset of N and i be an element of M, and denote by A (i, M) the event that i is the first element of M which occurs in an infinite sequence of outcomes. If Bj(i, M) denotes the event that the first (j1) outcomes are not in M and the jth outcome is i, one has
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