Jacques Peyri\`ere et les produits de Riesz.

link: http://arxiv.org/abs/1003.4600
Abstract

Jacques Peyri\`ere investigated Riesz products associated with a given set of
frequencies and the corresponding coefficients : mutual singularity or absolute
continuity of the measures defined by two such products, Hausdorff dimensions
of the sets carrying such measures, multifractal analysis. The present
expository paper starts from Peyri\`ere's results and give some new ways to
investigate the same questions. Since Riesz products are also an essential tool
for Sidon sets, the characterisations of Sidon sets by Pisier and Bourgain,
using quasi-independent sets, are given and commented. The paper ends with an
elementary construction of a <<big>> quasi-independent set. The paper is in
French. An introduction, in English, explains why it will not be published in
the book to which it was intended to contribute.