FILTRATION AND FINITE-DIMENSIONAL CHARACTERIZATION OF LOGARITHMICALLY CONVEX MEASURES


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Abstract

We study the classes C(α, β) and CH(α, β) of logarithmically convex measures that are a natural generalization of the notion of Boltzmann measure to an infinite-dimensional case. We prove a theorem on the characterization of these classes in terms of finite-dimensional projections of measures and describe some applications to the theory of random series.

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