  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.
