On the existence of the Stieltjes integral for functions of bounded variation |
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Authors: | T V Karataeva |
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Institution: | 1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev
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Abstract: | 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 values in a Banach algebra with identity regardless of the choice of points ξk ε tk?1, tk]. |
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