UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.2 43.1 42.2 42.1 41.2 41.1 40.2
40.1 39.2 39.1 38.2 38.1 37.2 37.1
36.2 36.1 35.2 35.1 34.2 34.1 33.2
33.1 32.2 32.1 31.2 31.1 30.2 30.1
29.2 29.1 28.2 28.1 27.2 27.1 26.2
26.1 25.2 25.1 24.2 24.1 23.2 23.1
22.2 22.1 21.2 21.1 20.2 20.1 19.2
19.1 18.2 18.1 17.2 17.1 16.2 16.1
15 14.2 14.1 13.2 13.1 12.2 12.1
11.2 11.1 10.2 10.1 9.2 9.1 8
7.2 7.1 6.2 6.1 5.2 5.1 4.2
4.1 3.2 3.1 2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 1, Fasc. 2,
pages 151 - 169
 

ON CONVERGENCE OF L1 -BOUNDED MARTINGALES INDEXED BY DIRECTED SETS

Annie Millet
Louis Sucheston

Abstract: Let (F ) t be an increasing family of s -algebras indexed by a directed set J. In this paper it is shown that every L 1 -bounded real-valued martingale converges essentially if and only if a weak type of maximal inequality holds for all martingales. A new covering condition C stated in terms of multivalued stopping times is introduced and characterized in terms of maximal inequalities. C is shown to be strictly weaker than the Vitali condition V, than SV (see [15]), and also sigma-SV. Under C, L 1 -bounded martingales taking values in a Banach space with the Radon-Nikodým property converge essentially.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

Download:    Abstract    Full text   Abstract + References