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 $B=l_p$. 
@article{IM2_1970_4_3_a8,
     author = {E. M. Nikishin},
     title = {On systems of convergence for~$l_p$},
     journal = {Izvestiya. Mathematics },
     pages = {627--644},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a8/}
}
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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/