منابع مشابه
Dilatation structures with the Radon-Nikodym property
The notion of a dilatation structure stemmed out from my efforts to understand basic results in sub-Riemannian geometry, especially the last section of the paper by Belläıche [2] and the intrinsic point of view of Gromov [5]. In these papers, as in other articles devoted to sub-Riemannian geometry, fundamental results admiting an intrinsic formulation were proved using differential geometry too...
متن کاملON THE RADON-NiKODYM-PROPERTY AND MARTINGALE CONVERGENCE
It is well-known that there is an intimate connection between the RadonNikodym property and martingale convergence in a Banach space. This connection can be "localized" to a closed bounded convex subset of a Banach space. In this paper we are interested primarily in this connection for a bounded convex set which is not closed. If C is a bounded convex set in a locally convex space, C is said to...
متن کاملThe near Radon-nikodym Property in Lebesgue-bochner Function Spaces
Let X be a Banach space and (Ω,Σ, λ) be a finite measure space, 1 ≤ p < ∞. It is shown that L(λ,X) has the Near Radon-Nikodym property if and only if X has it. Similarly if E is a Köthe function space that does not contain a copy of c0, then E(X) has the Near Radon-Nikodym property if and only if X does.
متن کاملSupport functionals and their relation to the Radon-Nikodym property
In this paper, we examine the Radon-Nikodym property and its relation to the Bishop-Phelps theorem for complex Banach spaces. We also show that the Radon-Nikodym property implies the Bishop-Phelps property in the complex case. 1. Introduction. Let X be a complex Banach space and let C be a closed convex subset of X. The set of support points of C, written as supp C, is the collection of all poi...
متن کاملOn Almost Sure Convergence without the Radon-nikodym Property
In this paper we obtain almost sure convergence theorems for vectorvalued uniform amarts and C-sequences without assuming the Radon-Nikodym Property. Specifically, it is shown that if a limit exists in a weak sense for these martingale generalizations, then a.s. scalar and strong convergence follow. These results lead to some new versions of the Ito-Nisio theorem. Convergence results for random...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1990
ISSN: 0263-6115
DOI: 10.1017/s1446788700030573