Geodesic
On systems of convergence for~$l_p$
Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 627-644.

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In this work, necessary and sufficient conditions are found in order for a system of measurable functions $\{f_n(x)\}$ to be a system of convergence for $l_p$. The assertions set forth here are a strengthening of the work of the author $({}^1)$ in the case when $B=l_p$. 
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     author = {E. M. Nikishin},
     title = {On systems of convergence for~$l_p$},
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E. M. Nikishin. On systems of convergence for~$l_p$. Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 627-644. http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a8/

[1] Nikishin E. M., “O sistemakh skhodimosti”, Matem. sb., 81(123) (1970), 23–38 | Zbl

[2] Nikishin E. M., “Odna teorema o funktsionalnykh posledovatelnostyakh”, Sib. matem. zh., XI:3 (1970)

[3] Kachmazh S., Shteingauz G., Teoriya ortogonalnykh ryadov, Fizmatgiz, M., 1958 | MR

[4] Aleksich G., Problemy skhodimosti ortogonalnykh ryadov, IL, M., 1963 | MR

[5] Nikishin E. M., “Dve teoremy o funktsionalnykh ryadakh”, Vestn. MGU, 1969, no. 6, 11–17 | Zbl

[6] Nikishin E. M., “O sistemakh absolyutnoi skhodimosti”, Matem. sb., 74(116) (1967), 544–553 | Zbl

[7] Vorobev N. N., Matrichnye igry, Sb. perevodov, Fizmatgiz, M., 1961 | MR

[8] Zigmund A., Trigonometricheskie ryady, t. II, Mir, M., 1965 | MR