On the existence of the Stieltjes integral for functions of bounded variation - Karataeva, T. V. (Ukrains’kyi Matematychnyi Zhurnal, 1995)
We obtain sufficient conditions of existence of the Stieltjes integral _s^t f(τ ) dF(τ ) = _δ _n → 0 _k = 1^m_n f(ξ _k )(F(t_k^n ) - F(t_k - 1^n )) for functions of bounded variation taking values in a Banach algebra with identity regardless of the choice of points ξ_k [t_k−1, t_k].