Denjoy–Khinchin-integrable functions and their conjugates

In this paper $2\pi$-periodic functions $\Phi(x)$ and $\Psi(x)$ are constructed so that they are both Denjoy–Khinchin integrable, are not equivalent to zero, and have conjugates $\overline\Phi$ and $\overline\Psi$ satisfying $\overline\Phi(x)=0$ almost everywhere and $\overline\Psi(x)=1$ almost everywhere.
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