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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] V. F. Gaposhkin, “Kriterii usilennogo zakona bolshikh chisel dlya klassov statsionarnykh protsessov i odnorodnykh sluchainykh polei”, DAN SSSR, 223:5 (1975), 1044–1047 | MR | Zbl

[2] Yu. K. Belyaev, “Analiticheskie sluchainye protsessy”, Teoriya veroyatnostei, IV:4 (1959), 437–444 | MR

[3] B. R. Levin, Teoreticheskie osnovy statisticheskoi radiotekhniki, t. 1, «Sov. radio», Moskva, 1974 | Zbl

[4] V. F. Gaposhkin, “Tochnye otsenki skorosti skhodimosti v usilennom zakone bolshikh chisel dlya klassov statsionarnykh v shirokom smysle posledovatelnostei i protsessov”, Uspekhi matem. nauk, XXXI:5 (191) (1976), 233–234

[5] A. Zigmund, Trigonometricheskie ryady, t. 1, Mir, Moskva, 1965

[6] A. M. Yurchenko, “Summirovanie kvaziortogonalnykh posledovatelnostei metodami Chezaro”, Analysis Math., 1:3 (1975), 231–237 | DOI | MR

[7] Z. A. Piranashvili, “K voprosu ob interpolyatsii sluchainykh protsessov”, Teoriya veroyatnostei, XII:4 (1967), 708–717

[8] Yu. A. Rozanov, “Spektralnyi analiz abstraktnykh funktsii”, Teoriya veroyatnostei, IV:3 (1959), 291–310

[9] G. G. Lorentz, “Über die Mittelwerte der Funktionen eines Orthogonalsystems”, Math. Z., 49 (1944), 724–733 | DOI | MR | Zbl