Some thoughts upon axiomatized languages with estension tools, a focus on probability theory and error calculus with Dirichlet forms

Details Some thoughts upon axiomatized languages with estension tools, a focus on probability theory and error calculus with Dirichlet forms Some thoughts upon axiomatized languages with estension tools, a focus on probability theory and error calculus with Dirichlet forms

2006-10-12

arxiv.org/abs/math/0610390v1

Butlleti de la Societat Catalana de Matematiques, 18, no 2 (2004) 25-36, Espagne (2004) 25-36

Mathematics

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Scientific paper

A comparison of the "theory of random sequences" developed during the twentieth century and the axiomatic approach of probability theory proposed by Kolmogorov shows the importance of sigma-additivity as extension tool. Similarly, the Cauchy criterion appears to be an extension tool for mathematical analysis. The Dirichlet forms theory possesses also such an extension tool. They are the source of the fruitfulness of these languages and the condition of their creativity. A connection is given with the so-called Richard paradox.

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