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Narrow Convergence in Spaces of Set-Valued Measures

Kenny Koffi Siggini (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

We prove an analogue of Topsøe's criterion for relative compactness of a family of probability measures which are regular with respect to a family sets. We consider measures whose values are compact convex sets in a locally convex linear topological space.

Notes on approximation in the Musielak-Orlicz sequence spaces of multifunctions

Andrzej Kasperski (1995)

Commentationes Mathematicae Universitatis Carolinae

We introduced the notion of ( 𝐗 , dist , 𝒱 ) -boundedness of a filtered family of operators in the Musielak-Orlicz sequence space X ϕ of multifunctions. This notion is used to get the convergence theorems for the families of 𝐗 -linear operators, 𝐗 -dist-sublinear operators and 𝐗 -dist-convex operators. Also, we prove that X ϕ is complete.

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