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Density questions in the classical theory of moments

Christian Berg;  J. P. Reus Christensen — 1981

Annales de l'institut Fourier

Let μ be a positive Radon measure on the real line having moments of all orders. We prove that the set P of polynomials is note dense in L p ( R , μ ) for any p > 2 , if μ is indeterminate. If μ is determinate, then P is dense in L p ( R , μ ) for 1 ≤ p ≤ 2 , but not necessarily for p > 2 . The compact convex set of positive Radon measures with same moments as μ is studied in some details.

Measurable functionals on function spaces

J. P. Reus Christensen;  J. K. Pachl — 1981

Annales de l'institut Fourier

We prove that all measurable functionals on certain function spaces are measures; this improves the (known) results about weak sequential completeness of spaces of measures. As an application, we prove several results of this form: if the space of invariant functionals on a function space is separable then every invariant functional is a measure.

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