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$$\int\limits_s^t {f(τ )} d\mathcal{F}(τ ) = \mathop {\lim }\limits_{δ _n → 0} \sum\limits_{k = 1}^{m_n } {f(ξ _k )(\mathcal{F}(t_k^n ) - \mathcal{F}(t_{k - 1}^n ))}$$for functions of bounded variation taking values in a Banach algebra with identity regardless of the choice of points $ξ_k \in [t_{k−1}, t_k]$.