Mengenwertige Masse und Fortsetzungen.
Mesures de Radon à valeurs vectorielles
Mesures vectorielles et partitions continues de l'unité
Moment Sequences in Locally Convex Spaces.
Monoidwertige Integrale
Monotone and convex -algebra valued functions.
Multilinear integration of bounded scalar valued functions
Multilinear operators on spaces
Given Banach spaces , and a compact Hausdorff space , we use polymeasures to give necessary conditions for a multilinear operator from into to be completely continuous (resp. unconditionally converging). We deduce necessary and sufficient conditions for to have the Schur property (resp. to contain no copy of ), and for to be scattered. This extends results concerning linear operators.
Near isometries of spaces of weak * continuous functions, with an application to Bochner spaces
New extension of the variational McShane integral of vector-valued functions
We define the Hake-variational McShane integral of Banach space valued functions defined on an open and bounded subset of -dimensional Euclidean space . It is a “natural” extension of the variational McShane integral (the strong McShane integral) from -dimensional closed non-degenerate intervals to open and bounded subsets of . We will show a theorem that characterizes the Hake-variational McShane integral in terms of the variational McShane integral. This theorem reduces the study of our...
Nonlinear integral operators on C(S,E)
Nonseparability of the quotient space cabv(∑,m;X)/L¹(m;X) for Banach spaces X without the Radon-Nikodym property
It is shown that if (S,∑,m) is an atomless finite measure space and X is a Banach space without the Radon-Nikodym property, then the quotient space cabv(∑,m;X)/L¹(m;X) is nonseparable.
Nonstandard Integration Theory in Topological Vector Lattices.
O integralnoj reprezentaciji linearnog operatora
On a Barrelled Space of Class ... and Measure Theory.
On a simultaneous selection theorem
Valov proved a general version of Arvanitakis's simultaneous selection theorem which is a common generalization of both Michael's selection theorem and Dugundji's extension theorem. We show that Valov's theorem can be extended by applying an argument by means of Pettis integrals due to Repovš, Semenov and Shchepin.
On certain barrelled normed spaces
Let be a -algebra on a set . If belongs to let be the characteristic function of . Let be the linear space generated by endowed with the topology of the uniform convergence. It is proved in this paper that if is an increasing sequence of subspaces of covering it, there is a positive integer such that is a dense barrelled subspace of , and some new results in measure theory are deduced from this fact.
On coincidence of Pettis and McShane integrability
R. Deville and J. Rodríguez proved that, for every Hilbert generated space , every Pettis integrable function is McShane integrable. R. Avilés, G. Plebanek, and J. Rodríguez constructed a weakly compactly generated Banach space and a scalarly null (hence Pettis integrable) function from into , which was not McShane integrable. We study here the mechanism behind the McShane integrability of scalarly negligible functions from (mostly) into spaces. We focus in more detail on the behavior...
On Compactness in L...(..., X) in the Weak Topology and in the Topology ...(L...(..., X), L...(..., X')).
On control submeasures and measures