1933 FoundationsOfTheTheoryOfProbability
- (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.
Notes
Cited By
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1986
- (Larsen & Marx, 1986) ⇒ Richard J. Larsen, and Morris L. Marx. (1986). “An Introduction to Mathematical Statistics and Its Applications, 2nd edition." Prentice Hall
- QUOTE: The next attempt at defining probability was entirely a product of the twentieth century. Modern mathematicians have shown a keen interest in developing subjects axiomatically. It was to be expected, then, that probability would come under such scrutiny … The major breakthrough on this front came in 1933 when Andrei Kolmogorov published Grundbegriffe der Wahscheinlichkeitsrechnung (Foundations of the Theory of Probability.). Kolmogorov's work was a masterpiece of mathematical elegance - it reduced the behavior of the probability function to a set of just three or four simple postulates, three if the same space is limited to a finite number of outcomes and four if [math]\displaystyle{ S }[/math] is infinite.
Quotes
... 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]. …
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| Author | volume | Date Value | title | type | journal | titleUrl | doi | note | year | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1933 FoundationsOfTheTheoryOfProbability | Andrei N. Kolmogorov | Grundbegriffe der Wahrscheinlichkeitsrechnung |