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On convergence of multiparameter strong submartingales in Banach lattices

О сходимости многопа раметрических сильн ых субмартингалов в банаховых решетках

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Abstract

В работе исследуются многопараметрическ ие субмартингалы со зна чениями в банахо-вых пространствах, сильн ые мартингалы и сильн ые субмартингалы.

Установлено, что еслиB - банахово пространс тво со свойством Радона—Ни кодима, то любойB-зяачный рав номерно интегрируем ый сильный мартингал {M n ,n∈N d} почти наверное сходится пр иn→∞.

С помощью этой теорем ы изучается сходимос ть сильных субмартингалов со зн ачениями в банаховой решетке.

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  1. Department of Mathematics, Kossuth Lajos University, 4010, Debrecen PF. 12, Hungary

    István Fazekas

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  1. István Fazekas
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Fazekas, I. On convergence of multiparameter strong submartingales in Banach lattices. Analysis Mathematica 10, 207–212 (1984). https://doi.org/10.1007/BF01917634

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  • DOI: https://doi.org/10.1007/BF01917634

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