On the existence of the Stieltjes integral (Q1385860)

The paper includes several theorems concerning the existence of the Hellinger integral. As corollaries, the author has obtained results about the Stieltjes integral. A typical example is Theorem 2: For a function \(f\) which is Riemann integrable the following conditions are equivalent: 1) the Hellinger integral \(I_H(f,g)\) exists for all \(g\) of bounded \(\Phi\)-variation, 2) the Hellinger integral \(I_H(f, g)\) exists for all \(\Phi\)-continuous \(g\).