Abstract
Based on results from the theory of ordered (topological) vector spaces and on the theory of Fourier transforms of Radon probability measures (Bochner–Minlos–Schwartz) we present a solution of infinite dimensional moment problems over real nuclear spaces E. Both moment and truncated moment problems are treated simultaneously. In both cases uniqueness of the representing measure is characterized in terms of conditions on the set of moments directly. Concentration of the representing measures is expressed through continuity properties of the second moment. This is finally applied to characterize weak convergence of sequences of measures in terms of pointwise convergence of the associated sequence of moment functionals on the tensor algebra over E.
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