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Currently displaying 1 – 3 of 3

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Small sets and a class of general functions.

J.-P. Reus Christensen; Pal Fischer — 1987

Aequationes mathematicae

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 $1 \leq p \leq 2$ , 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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