Geodesic
Remarks on correcting
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIII, Tome 135 (1984), pp. 69-75

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The paper consists of two sections. In the first one it is proved that any bounded non-nogative lower semi-continuous function on the unit circle is the modulus of some function with uniformly bounded Fourier sums. In the second section a simple proof of the following known result is presented: given a measurable function $f$ on the unit circle and $\varepsilon>0$, a function can be found so that $m\{f\ne g\}\varepsilon$ and the Fourier series of ($g$ with respect to the trigonometric system and to the Walsh system converge uniformly. 
@article{ZNSL_1984_135_a5,
     author = {S. V. Kislyakov},
     title = {Remarks on correcting},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {69--75},
     publisher = {mathdoc},
     volume = {135},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_135_a5/}
}
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S. V. Kislyakov. Remarks on correcting. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIII, Tome 135 (1984), pp. 69-75. http://geodesic.mathdoc.fr/item/ZNSL_1984_135_a5/