Geodesic
Limits of indeterminacy in measure of $T$-means of trigonometric series
Sbornik. Mathematics, Tome 10 (1970) no. 4, pp. 441-474

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

The following theorem is proved. Let $F(x)$ and $G(x)$ be arbitrary measurable functions such that $G(x)\leqslant F(x)$ almost everywhere on $[-\pi,\pi]$, and let $T$ be an arbitrary row-finite summation method defined by a real matrix. Then there exists a trigonometric series whose coefficients tend to zero and such that the limits of indeterminacy of its $T$-means are exactly $F(x)$ and $G(x)$. Bibliography: 8 titles. 
@article{SM_1970_10_4_a0,
     author = {D. E. Men'shov},
     title = {Limits of indeterminacy in measure of $T$-means of trigonometric series},
     journal = {Sbornik. Mathematics},
     pages = {441--474},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_10_4_a0/}
}
TY  - JOUR
AU  - D. E. Men'shov
TI  - Limits of indeterminacy in measure of $T$-means of trigonometric series
JO  - Sbornik. Mathematics
PY  - 1970
SP  - 441
EP  - 474
VL  - 10
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1970_10_4_a0/
LA  - en
ID  - SM_1970_10_4_a0
ER  - 
%0 Journal Article
%A D. E. Men'shov
%T Limits of indeterminacy in measure of $T$-means of trigonometric series
%J Sbornik. Mathematics
%D 1970
%P 441-474
%V 10
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1970_10_4_a0/
%G en
%F SM_1970_10_4_a0
D. E. Men'shov. Limits of indeterminacy in measure of $T$-means of trigonometric series. Sbornik. Mathematics, Tome 10 (1970) no. 4, pp. 441-474. http://geodesic.mathdoc.fr/item/SM_1970_10_4_a0/