In recent years, convergence results for multivalued functions have been developed and used in several areas of applied mathematics: mathematical economics, optimal control, mechanics, etc. The aim of this note is to give a criterion of almost sure convergence for multivalued asymptotic martingales (amarts). For every separable Banach space B the fact that every L¹-bounded B-valued martingale converges a.s. in norm to an integrable B-valued random variable (r.v.) is equivalent to the Radon-Nikodym property [6]. In this paper we solve the problem of a.s. convergence of multivalued amarts by giving a topological characterization.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-1-10,
author = {Dorota Dudek and Wies\l aw Zi\k eba},
title = {On Multivalued Amarts},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {52},
year = {2004},
pages = {93-99},
zbl = {1097.60028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-1-10}
}
Dorota Dudek; Wiesław Zięba. On Multivalued Amarts. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) pp. 93-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-1-10/