A NEW APPROACH TO THE FOUNDATIONS OF PROBABILITY.
Technical rept. no. 4,
MICHIGAN STATE UNIV EAST LANSING
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In the history of the theory of probability, until recently there was no suitable foundational system on which probability calculations could be based which would yield satisfactory results. The first formulation which was adequate for general probability computations, and the only one now in wide use, is that of Kolmogoroff. However, the author claims that it is not altogether satisfactory, and gives an alternative formulation, along with showing the relationships and differences of the two approaches. The alternative formulation of probability theory is in the Von Neumann-Bernays-Godel set theory, and preserves all the theorems of the Kolmogoroff formulation. The only new results are those involving proper classes. Properties from the Kolmogoroff formulation are obtained which serve as an axiom system, and one additional axiom is added.