Geodesic
Diagonal martingale ergodic sequences
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 2, pp. 103-107

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A proof of convergence almost everywhere for diagonal martingale ergodic sequences which include ergodic averages and Cesaro averages for reversed martingale as special cases is obtained in the article. A condition of mutual commuting for conditional expectations and ergodic averaging is sufficient for this convergence. Maximal and dominant inequalities also are proved for such sequences.
Keywords: martingale ergodic sequence, reversed martingale, ergodic averages, Dunford–Schwartz operator. 
@article{VNGU_2012_12_2_a8,
     author = {I. V. Podvigin},
     title = {Diagonal martingale ergodic sequences},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {103--107},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2012_12_2_a8/}
}
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I. V. Podvigin. Diagonal martingale ergodic sequences. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 2, pp. 103-107. http://geodesic.mathdoc.fr/item/VNGU_2012_12_2_a8/