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.