A Note on the Concept of Independence

Elart von Collani
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Elart von Collani: University of Würzburg, Sanderring 2, D-97070 Würzburg, Germany

Stochastics and Quality Control, 2006, vol. 21, issue 1, 155-164

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.

Date: 2006
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DOI: 10.1515/EQC.2006.155

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