Vol. 87, No. 2, 1980

Recent Issues
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
The Radon-Nikodým property, σ-dentability and martingales in locally convex spaces

Leo Egghe

Vol. 87 (1980), No. 2, 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 σ-dentability. (RNP) is equivalent with the property that a certain class of martingales is mean convergent, while σ-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 integrable functions, the range space being sequentially complete.

Mathematical Subject Classification 2000
Primary: 46E40
Secondary: 46A99
Milestones
Received: 2 November 1978
Revised: 8 March 1979
Published: 1 April 1980
Authors
Leo Egghe