Some thoughts upon axiomatized languages with estension tools, a focus on probability theory and error calculus with Dirichlet forms
History and Overview
2007-05-23 v1 Probability
Abstract
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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Cite
@article{arxiv.math/0610390,
title = {Some thoughts upon axiomatized languages with estension tools, a focus on probability theory and error calculus with Dirichlet forms},
author = {Nicolas Bouleau},
journal= {arXiv preprint arXiv:math/0610390},
year = {2007}
}