Menshov's ``adjustment theorem'' with respect to general measures (Q515526)

The author of the paper under review suggests the following Theorem. If \( f:[0,2\pi] \rightarrow \mathbb{R} \) is Borel measurable and \(\mu\) is a positive, finite Borel measure on \([0,2\pi]\), then, for every \(\varepsilon >0 \), there exists a~continuous \( g:[0,2\pi] \rightarrow \mathbb{R}\) with uniformly convergent Fourier series so that \(\mu(\{ f\neq g\})< \varepsilon\).