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A History of the Central Limit TheoremConclusion: The Central Limit Theorem as a Link Between Classical and Modern Probability Theory

A History of the Central Limit Theorem: Conclusion: The Central Limit Theorem as a Link Between... [During the period between the two world wars, modern probability theory emerged as a mathematical subdiscipline—with the typical formation of concepts, main theorems and methods—by integrating the subfields of axiomatics (including aspects of measure theory), strong laws of large numbers, stochastic processes, and limit theorems for distributions of sums of random variables, which at first were related by little more than the shared generic term “probability.” Only this last field of limit theorems could point to any significant contributions in the 18th and particularly the 19th centuries, and it played an especially important role during the transition from classical to modern probability theory. In the following summary of the most important aspects of this book, that role will be examined more closely. In so doing, it is particularly important to pursue the question of how the CLT can be understood as “classical” content of probability theory and what types of changes it underwent while crossing over to modern probability.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A History of the Central Limit TheoremConclusion: The Central Limit Theorem as a Link Between Classical and Modern Probability Theory

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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10 pages

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Publisher
Springer New York
Copyright
© Springer Science+Business Media, LLC 2011
ISBN
978-0-387-87856-0
Pages
353 –362
DOI
10.1007/978-0-387-87857-7_8
Publisher site
See Chapter on Publisher Site

Abstract

[During the period between the two world wars, modern probability theory emerged as a mathematical subdiscipline—with the typical formation of concepts, main theorems and methods—by integrating the subfields of axiomatics (including aspects of measure theory), strong laws of large numbers, stochastic processes, and limit theorems for distributions of sums of random variables, which at first were related by little more than the shared generic term “probability.” Only this last field of limit theorems could point to any significant contributions in the 18th and particularly the 19th centuries, and it played an especially important role during the transition from classical to modern probability theory. In the following summary of the most important aspects of this book, that role will be examined more closely. In so doing, it is particularly important to pursue the question of how the CLT can be understood as “classical” content of probability theory and what types of changes it underwent while crossing over to modern probability.]

Published: Aug 21, 2010

Keywords: Probability Theory; Limit Theorem; Independent Random Variable; Limit Distribution; Limit Problem

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