Geodesic
Representation of measurable functions by orthogonal series
Sbornik. Mathematics, Tome 27 (1975) no. 1, pp. 93-102 
N. B. Pogosyan. Representation of measurable functions by orthogonal series. Sbornik. Mathematics, Tome 27 (1975) no. 1, pp. 93-102. http://geodesic.mathdoc.fr/item/SM_1975_27_1_a7/
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     title = {Representation of measurable functions by orthogonal series},
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     url = {http://geodesic.mathdoc.fr/item/SM_1975_27_1_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper it is proved that for each bounded orthonormal system $\{\varphi_n(x)\}$ complete in $L^2[0,1]$ there is a series $\sum_{n=1}^\infty a_n\varphi_n(x)$ having the property that for each measurable function $F(x)$ ($F(x)$ can assume infinite values) the terms of the series $\sum_{n=1}^\infty a_n\varphi_n(x)$ can be rearranged so that the resultant series converges almost everywhere to $F(x)$. Bibliography: 5 titles.

[1] N. K. Bari, Trigonometricheskie ryady, Fizmatgiz, Moskva, 1961 | MR

[2] A. A. Talalyan, “Predstavlenie izmerimykh funktsii ryadami”, Uspekhi matem. nauk, XV:5(100) (1960), 77–141 | MR

[3] P. L. Ulyanov, “O bezuslovnoi skhodimosti i summiruemosti”, Izv. AN SSSR, seriya matem., 22 (1958), 811–840 | MR

[4] R. Kuk, Beskonechnye matritsy i prostranstva posledovatelnostei, Fizmatgiz, Moskva, 1960

[5] A. Garsia, Topics in almost everywhere convergence, Markham, Chicago, 1970 | MR | Zbl