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http://hdl.handle.net/1942/17903
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. | Document URI: | http://hdl.handle.net/1942/17903 | Link to publication/dataset: | http://projecteuclid.org/euclid.pjm/1102779968 | ISSN: | 0030-8730 | e-ISSN: | 1945-5844 | Category: | A2 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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