Sur le caractere gaussien de la convergence presque partout

Volume 167 / 2001

Michel Weber Fundamenta Mathematicae 167 (2001), 23-54 MSC: Primary 28D05, 60G15; Secondary 26D07, 60G17. DOI: 10.4064/fm167-1-3


We establish functional type inequalities linking the regularity properties of sequences of operators $S=(S_n)$ acting on $L^2$-spaces with those of the canonical Gaussian process on the associated subsets of $L^2$ defined by $(S_n(f))$, $f\in L^2$. These inequalities allow us to easily deduce as corollaries Bourgain's famous entropy criteria in the theory of almost everywhere convergence. They also provide a better understanding of the role of the Gaussian processes in the study of almost everywhere convergence. A partial converse path to Bourgain's entropy criteria is also proposed.


  • Michel WeberMathématique (IRMA)
    Université Louis-Pasteur
    7, rue René Descartes
    67084 Strasbourg Cedex, France

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