A New Approach to the Foundations of Probability

  • Herman Rubin


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 use1, is that of Kolmogoroff. However, we claim that it is not altogether satisfactory, and we shall give an alternative formulation, and show the relationships and differences of the two approaches.


Measurable Function Sample Space Division Ring Minimal Pair Homomorphism Property 
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    Blackwell, D., and M. A. Girshick: Theory of games and statistical decisions. New York: Wiley 1954.MATHGoogle Scholar
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    Gödel, K.: The consistency of the continuum hypothesis. Ann. Math. Studies No. 3, Princeton: 1940.MATHGoogle Scholar
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    Kolmogoroff, A.: Grundbegriffe der Wahrscheinlichkeitsrechnung. Ergebn. Mathematik 2, 3 (1933).Google Scholar
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    Lehmann, E. L.: Testing statistical hypotheses. New York: Wiley 1959.MATHGoogle Scholar

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© Springer-Verlag Berlin · Heidelberg 1969

Authors and Affiliations

  • Herman Rubin

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