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A History of the Central Limit TheoremThe Way Toward Modern Probability

A History of the Central Limit Theorem: The Way Toward Modern Probability [Richard von Mises [1919a, 1] wrote in his pioneering paper “Fundamentalsätze der Wahrscheinlichkeitsrechnung”: The analytical theorems of probability theory are lacking—except for a few works by Russian mathematicians—the precision of formulation and reasoning which has long been a matter of course in other areas of analysis. And in spite of some valuable approaches, these days there is still an almost complete lack of clarity about the foundations of probability theory as a mathematical discipline. VonMises dealt with the problem of the axiomatic foundations of probability theory by a frequentistic approach in another article [1919b], which has achieved greate prominence today than the one that preceded it.1 In his criticism of the inadequate fundamentals of probability theory, von Mises alluded to the lecture David Hilbert had delivered before the 2nd International Congress of Mathematicians, held in Paris in 1900, in which Hilbert had presented “his” 23 problems. The sixth problem related to the “mathematical treatment of the axioms of physics.”] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A History of the Central Limit TheoremThe Way Toward Modern Probability

Part of the Sources and Studies in the History of Mathematics and Physical Sciences Book Series
Fischer, Hans
Springer Journals — Aug 21, 2010
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79 pages

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Publisher
Springer New York
Copyright
© Springer Science+Business Media, LLC 2011
ISBN
978-0-387-87856-0
Pages
191 –269
DOI
10.1007/978-0-387-87857-7_5
Publisher site
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Abstract

[Richard von Mises [1919a, 1] wrote in his pioneering paper “Fundamentalsätze der Wahrscheinlichkeitsrechnung”: The analytical theorems of probability theory are lacking—except for a few works by Russian mathematicians—the precision of formulation and reasoning which has long been a matter of course in other areas of analysis. And in spite of some valuable approaches, these days there is still an almost complete lack of clarity about the foundations of probability theory as a mathematical discipline. VonMises dealt with the problem of the axiomatic foundations of probability theory by a frequentistic approach in another article [1919b], which has achieved greate prominence today than the one that preceded it.1 In his criticism of the inadequate fundamentals of probability theory, von Mises alluded to the lecture David Hilbert had delivered before the 2nd International Congress of Mathematicians, held in Paris in 1900, in which Hilbert had presented “his” 23 problems. The sixth problem related to the “mathematical treatment of the axioms of physics.”]

Published: Aug 21, 2010

Keywords: Characteristic Function; Central Limit Theorem; Independent Random Variable; Stable Distribution; Elementary Error

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