Abstract
Based on the total H$_{1}$-integrability concept, which is established in this paper, we shall try to show that at any point of a compact interval $(a,b]$ in $\mathbb{R}$, at which a point function $F$ has no a discontinuity, $F$ is the total H$_{1}$-indefinite integral of a function $dF_{ex}$ being the limit of $\Delta F_{ex}(I)$, where $I \subseteq [a,b]$, on $[a,b]$, without additional hypotheses on $F$. A residue function of $F$ is introduced. The paper ends with a few of examples that illustrate the theory.
Citation
Branko Sarić. "On Totalization of the $H_1$-Integral." Taiwanese J. Math. 15 (4) 1691 - 1700, 2011. https://doi.org/10.11650/twjm/1500406373
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