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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/17934

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.
URI: http://hdl.handle.net/1942/17934
DOI: 10.1007/BFb0069664
ISBN: 978-3-540-08669-7
ISSN: 0075-8434
Category: B2
Type: Book Section
Appears in Collections: Research publications

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