Geodesic
Limits of indeterminacy in measure of $T$-means of trigonometric series
Sbornik. Mathematics, Tome 10 (1970) no. 4, pp. 441-474 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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