Kislyakov, S. V. Remarks concerning a ”correction”. (Russian. English summary) Zbl 0536.42008 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 135, 69-75 (1984). This paper points out that any bounded non-negative lower semi-continuous function on the unit circle is the modulus of some function with uniformly bounded Fourier sums and gives a simple proof of the following known result: Given a measurable function f on the unit circle and \(\epsilon>0\), a function g can be found so that \(m\{f\neq g\}<\epsilon\) and the Fourier series of g converges uniformly. Reviewer: W.Yang Cited in 1 ReviewCited in 2 Documents MSC: 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) Keywords:bounded; lower semi-continuous; measurable; uniformly bounded Fourier sums PDFBibTeX XMLCite \textit{S. V. Kislyakov}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 135, 69--75 (1984; Zbl 0536.42008) Full Text: EuDML