Filtration and Finite-Dimensional Characterization of Logarithmically Convex Measures

We study the classes C(, ) and C _H(, ) 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.