Geodesic
The Hardy--Littlewood problem for regular and uniformly distributed number sequences
Izvestiya. Mathematics , Tome 44 (1995) no. 2, pp. 359-371

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

Let $H$ be the set of functions $f(x)$ defined in $(0, 1)$, $f(0+0)=f(1-0)=+\infty$, monotone in neighborhoods of singular points and such that the improper Riemann integral $\int\limits_0^1f(x)\,dx$ converges. Let $Q$ be an arbitrary set of sequences $(\{x_i\})_{i=1}^\infty$ uniformly distributed in the interval $[0, 1]$. We find the set of those pairs in $H\times Q$ for which the following equality is valid: $$ \lim\limits_{n\to\infty}\frac{1}{n}\sum_{i=1}^n f(\{x_i\})=\int\limits_0^1f(x)\,dx. $$ 
@article{IM2_1995_44_2_a7,
     author = {V. A. Oskolkov},
     title = {The {Hardy--Littlewood} problem for regular and uniformly distributed number sequences},
     journal = {Izvestiya. Mathematics },
     pages = {359--371},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_44_2_a7/}
}
TY  - JOUR
AU  - V. A. Oskolkov
TI  - The Hardy--Littlewood problem for regular and uniformly distributed number sequences
JO  - Izvestiya. Mathematics 
PY  - 1995
SP  - 359
EP  - 371
VL  - 44
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1995_44_2_a7/
LA  - en
ID  - IM2_1995_44_2_a7
ER  - 
%0 Journal Article
%A V. A. Oskolkov
%T The Hardy--Littlewood problem for regular and uniformly distributed number sequences
%J Izvestiya. Mathematics 
%D 1995
%P 359-371
%V 44
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1995_44_2_a7/
%G en
%F IM2_1995_44_2_a7
V. A. Oskolkov. The Hardy--Littlewood problem for regular and uniformly distributed number sequences. Izvestiya. Mathematics , Tome 44 (1995) no. 2, pp. 359-371. http://geodesic.mathdoc.fr/item/IM2_1995_44_2_a7/