LIMITS OF INDETERMINACY IN MEASURE OFT-MEANS OF TRIGONOMETRIC SERIES
D. E. Men′šov · Mathematics of the USSR-Sbornik · 1970
The following theorem is proved. Let F(x) and G(x) be arbitrary measurable functions such that G(x)?F(x) almost everywhere on [- ?,??], 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 items.