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date: 25 January 2020

Abstract and Keywords

In the 18th and 19th centuries, probability was a part of moral and natural sciences, rather than of mathematics. Still, since Laplace’s 1812 Théorie analytique des probabilités, specific analytic methods of probability aroused the interest of mathematicians, and probability began to develop a purely mathematical quality. In the 20th century the mathematical essence reached full autonomy and constituted “modern” probability. Significant in this development was the gradual introduction of a measure theoretic framework. In this way, the main subfields of modern probability, as axiomatics, weak and strong limit theorems, sequences of non-independent random variables, and stochastic processes, could be integrated into a well-connected complex until World War II.

Keywords: Laplace, error theory, kinetic theory of gases, sum of random variables, weak limit theorem, law of large numbers, non-independent random variable, stochastic process, axiomatics, measure theory

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