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Remarks concerning a ”correction”. (Russian. English summary) Zbl 0536.42008

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

MSC:

42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
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