On the existence of the Stieltjes integral for functions of bounded variation

• Datum: 1995
• Hauptverfasser: Karataeva, T. V., Каратаева, Т. В.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 1995
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/5438
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We obtain sufficient conditions of existence of the Stieltjes integral $$\int\limits_s^t {f(\tau )} d\mathcal{F}(\tau ) = \mathop {\lim }\limits_{\delta _n \to 0} \sum\limits_{k = 1}^{m_n } {f(\xi _k )(\mathcal{F}(t_k^n ) - \mathcal{F}(t_{k - 1}^n ))}$$ for functions of bounded variation taking va...