Geodesic
Series of a system ${\varphi(nx)}$
Matematičeskie zametki, Tome 5 (1969) no. 5, pp. 527-532 
E. M. Nikishin. Series of a system ${\varphi(nx)}$. Matematičeskie zametki, Tome 5 (1969) no. 5, pp. 527-532. http://geodesic.mathdoc.fr/item/MZM_1969_5_5_a3/
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     author = {E. M. Nikishin},
     title = {Series of a~system ${\varphi(nx)}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {527--532},
     year = {1969},
     volume = {5},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_5_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Several theorems on series of systems $\{\varphi(nx)\}$ are proved. It is shown, in particular, that there exists a continuous function $\varphi(x)$ such that a series of the system $\{\varphi(2^nx)\}$ with coefficients in $l_2$ does not converge in measure on $[0,1]$. This provides the answer to a problem raised by P. L. Ul'yanov.