Convergence of vector valued plurisubharmonic martingales with two indices
type: Item
instance of: scholarly article
title: Convergence of vector valued plurisubharmonic martingales with two indices
zbMATH Open document ID: 0792.46009
author: Mohamed Daher
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 1993-05-16T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73292
review text: In [\textit{A. V. Bukhvalov} and \textit{A. A. Danilevich}, Math. Notes, 31, 104-110 (1982; Zbl 0496.30029)], the notion of a (complex) Banach space \(X\) with the analytic Radon-Nikodym property was introduced. The analytic Radon-Nikodym property is equivalent to an a.s. convergence theorem for pluri-subharmonic martingales (cf. the above reference), like the classical Radon-Nikodym property is equivalent to the fulfillment of the Doob martingale convergence theorem. In this paper, among other characterizations and ramifications, it is proved that the analytic Radon-Nikodym property holds whenever the corresponding convergence theorem is valid for pluri-subharmonic martingales with two indices.
Mathematics Subject Classification ID: 46B22
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 46G10
zbMATH DE Number: 168576
zbMATH Keywords: analytic Radon-Nikodym property
zbMATH Keywords: a.s. convergence theorem for pluri- subharmonic martingales
zbMATH Keywords: Doob martingale convergence theorem
reviewed by: Jerzy Szulga
MaRDI profile type: Publication
OpenAlex ID: W2027740555
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DOI: 10.5802/AFST.736
description: scientific article; zbMATH DE number 168576