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A Note on the Concept of Independence

Author

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  • von Collani Elart

    (University of Würzburg, Sanderring 2, D-97070 Würzburg, Germany)

Abstract

In 1933 A.N. Kolmogorov's famous essay Grundbegriffe der Wahrscheinlichkeitsrechnung was published by the publisher Julius Springer in Berlin. It contained an axiomatization of probability theory and led to an unimagined upturn of probability theory and its application. Especially the effect on application must surprise because based on the the axioms, probability theory had become a genuine part of mathematics without any concrete real-world meaning. Kolmogorov states himself about the field of probabilities: “What the elements of this set represent is of no importance in the purely mathematical development of the theory of probability.” In his treatise Kolmogorov also deals with the concept of independence and introduces it as a purely mathematical quantity without regarding any real-world meaning. In this paper it is shown that the mathematical concept of independence of events is inappropriate from a more realistic point of view.

Suggested Citation

  • von Collani Elart, 2006. "A Note on the Concept of Independence," Stochastics and Quality Control, De Gruyter, vol. 21(1), pages 155-164, January.
    • Handle: RePEc:bpj:ecqcon:v:21:y:2006:i:1:p:155-164:n:5
    DOI: 10.1515/EQC.2006.155
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