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On B r -completeness

Manuel Valdivia (1975)

Annales de l'institut Fourier

In this paper it is proved that if { E n } n = 1 and { F n } n = 1 are two sequences of infinite-dimensional Banach spaces then H = n = 1 E n × n = 1 F n is not B r -complete. If { E n } n = 1 and { F n } n = 1 are also reflexive spaces there is on H a separated locally convex topology , coarser than the initial one, such that H [ ] is a bornological barrelled space which is not an inductive limit of Baire spaces. It is given also another results on B r -completeness and bornological spaces.

On some aspects of Jensen-Menger convexity.

Joanna Ger, Roman Ger (1992)

Stochastica

The paper contains various results concerning the so-called homogeneity sets for convex functions defined on convex subsets of some special metric spaces named G-space (cf. H. Busemann [1]). A closed graph theorem for such type mappings is also presented.

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