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Title: The Radon-Nikodym-Property, σ-dentability and martingales in locally convex spaces.
Authors: EGGHE, Leo 
Issue Date: 1980
Source: PACIFIC JOURNAL OF MATHEMATICS, 87 (2), p. 313-322
Abstract: In this paper we give relations between the Radon Nikodym-Property (RNP), in sequentially complete locally convex spaces, mean convergence of martingales, and α-dentability. (RNP) is equivalent with the property that a certain class of martingales is mean convergent, while <7-dentability is equivalent with the property that the same class of martingales is mean Cauchy. We give an example of a σ-dentable space not having the (RNP). It is also an example of a sequentially incomplete space of in tegrable functions, the range space being sequentially complete.
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ISSN: 0030-8730
e-ISSN: ****-****
Category: A2
Type: Journal Contribution
Appears in Collections:Research publications

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