Geodesic
The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces
Kybernetika, Tome 48 (2012) no. 2, pp. 254-267.

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We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.
Classification : 60B12, 60E15, 60F15, 60G42
Keywords: the Doob inequality; strong law of large numbers; martingale difference array; Banach space 
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     author = {Huan, Nguyen Van and Quang, Nguyen Van},
     title = {The {Doob} inequality and strong law of large numbers for multidimensional arrays in general {Banach} spaces},
     journal = {Kybernetika},
     pages = {254--267},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2012},
     mrnumber = {2954324},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_2_a5/}
}
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Huan, Nguyen Van; Quang, Nguyen Van. The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces. Kybernetika, Tome 48 (2012) no. 2, pp. 254-267. http://geodesic.mathdoc.fr/item/KYB_2012__48_2_a5/