1933 FoundationsOfTheTheoryOfProbability

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  • (Kolmogorov, 1933) ⇒ Andrei Kolmogorov. (1933). “Grundbegriffe der Wahrscheinlichkeitsrechnung.” (Foundations of the Theory of Probability.). American Mathematical Society. ISBN:0828400237

Subject Headings: Kolmogorov Probability Function Axiom, Probability Function.


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... Given a mapping of the set [math]\displaystyle{ E }[/math] into a set [math]\displaystyle{ E' }[/math] consisting of any type of elements, i.e., a single-valued function [math]\displaystyle{ u(e) }[/math] defined on [math]\displaystyle{ E }[/math], whose values belong to [math]\displaystyle{ E' }[/math]. To each subset [math]\displaystyle{ A' }[/math] of [math]\displaystyle{ E' }[/math] we shall put …

... Every distributions function [math]\displaystyle{ F_{\mu_1 \mu_2 … \mu_n} }[/math], satisfying the general conditions of Chap. II, Sec 3, III and also conditions (2) and (3). Every distribution function [math]\displaystyle{ F_{\mu_1 \mu_2 … \mu_n} }[/math] defines uniquely a corresponding probability function [math]\displaystyle{ \text{P}_{\mu_1 \mu_2 … \mu_n} }[/math] for all Borel sets of [math]\displaystyle{ R^n }[/math]. …


 AuthorvolumeDate ValuetitletypejournaltitleUrldoinoteyear
1933 FoundationsOfTheTheoryOfProbabilityAndrei N. KolmogorovGrundbegriffe der Wahrscheinlichkeitsrechnung