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.
Publié le : 2004-07-05
Classification:
Kolmogorov,
random number,
random sequence,
sigma-additivity,
Dirichlet forms,
Cauchy criterion,
Richard paradox,
MSC 01A61 03D99 31C25 60-03 60A05,
[MATH.MATH-HO]Mathematics [math]/History and Overview [math.HO],
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00105636,
author = {Bouleau, Nicolas},
title = {Some thoughts upon axiomatized languages with extension tools, a focus on probability theory and error calculus with Dirichlet forms},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00105636}
}
Bouleau, Nicolas. Some thoughts upon axiomatized languages with extension tools, a focus on probability theory and error calculus with Dirichlet forms. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00105636/