  We study various Stieltjes integrals as Poisson-Stieltjes, conjugate
Poisson-Stieltjes, Schwartz-Stieltjes and Cauchy-Stieltjes and prove theorems
on the existence of their finite angular limits a.e. in terms of the singular
Hilbert-Stieltjes integral in the sense of the principal value. These results
hold for arbitrary $2\pi -$periodic bounded integrands that are differentiable
a.e. and, in particular, for integrands of the class ${\cal {CBV}}$ (countably
bounded variation).

Complex Variables