On functions of generalized bounded variation

A theorem is proved on passage to a limit under the sign of a Perron–Stieltjes integral, and it is used to obtain several other theorems, one of which is the following.
Theorem. If $\Phi$ and its conjugate $\overline\Phi$ are functions of generalized bounded variation in the narrow sense on $[0,2\pi)$ that do not have discontinuities of the second kind nor removable discontinuities (that is, left-hand and right-hand limits exist at each point, and they do not coincide at a point of discontinuity), then $\Phi$ and $\overline\Phi$ are absolutely continuous functions in the generalized narrow sense on $[0,2\pi)$.
It is shown that the results cannot be strengthened.
Bibliography: 14 titles.