Limits of indeterminacy in measure of $T$-means of trigonometric series

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 $G(x)$.
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