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|Title: ||On the Radon-Nikodym-Property, and related topics in locally convex spaces|
|Authors: ||EGGHE, Leo|
|Issue Date: ||1978|
|Publisher: ||Springer Berlin Heidelberg|
|Citation: ||Aron, Richard M.; Dineen, Seán (Ed.). Vector Space Measures and Applications II, p. 77-90|
|Series/Report: ||Lecture Notes in Mathematics|
|Series/Report no.: ||645|
|Abstract: ||We introduce L X 1 (μ), the space of classes of X-valued μ-integrable functions used by Saab, which is an extension of the space of classes of Bochner-integrable functions, in Banach spaces. X denotes here a sequentially complete locally convex space.
We give examples of spaces which are dentable, σ-dentable, having the Radon-Nikodym-Property, or having the Bishop-Phelps-Property, by proving some projective limit results.
We also prove the following theorem : The following implications are valid : TeX
1.X has the Radon-Nikodym-Property.
2.Every uniformly bounded martingale is L X 1 -convergent.
3.Every uniformly bounded martingale is L X 1 -Cauchy.
4.Every uniformly bounded and finitely generated martingale is L X 1 -Cauchy.
5.X is σ-dentable.
So we have the equivalency of (i) through (v) for quasi-complete (BM)-spaces.|
|Type: ||Book Section|
|Appears in Collections: ||Research publications|
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