Geodesic
A~theorem on the convergence almost everywhere of a~sequence of measurable functions, and its applications to sequences of stochastic integrals
Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 1-17

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It is shown that various problems on the convergence almost everywhere of sequences of stochastic integrals (the theorem of Kotel'nikov for stationary processes, estimates of the means of stationary processes and homogeneous fields) can be solved with the help of a general theorem on convergence of a sequence of measurable functions. Bibliography: 9 titles. 
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V. F. Gaposhkin. A~theorem on the convergence almost everywhere of a~sequence of measurable functions, and its applications to sequences of stochastic integrals. Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/SM_1977_33_1_a0/