Some consequences of a kind of Hahn-Banach's theorem

Richard Becker

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Infinitely divisible measures on the cone of an ordered locally convex vector spaces

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Annales scientifiques de l'Université de Clermont. Mathématiques

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Every conical measure on a weak complete space $E$ is represented as integration with respect to a $σ$ -additive measure on the cylindrical $σ$ -algebra in $E$ . The connection between conical measures on $E$ and $E$ -valued measures gives then some sufficient conditions for the representing measure to be finite.

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The Radon spaces of type (T), i.e., topological spaces for which every finite Borel measure on Omega is T-additive and T-regular are characterized. The class of these spaces is very wide and in particular it contains the Radon spaces. We extend the results of Marczewski an Sikorski to the sygma-metrizable spaces and to the subsets of the Banach spaces endowed with the weak topology. Finally, the completely additive families of measurable subsets related with the works of Hansell, Koumoullis,...