Taiwanese Journal of Mathematics

On Totalization of the $H_1$-Integral

Branko Sarić

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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.

Article information

Source
Taiwanese J. Math., Volume 15, Number 4 (2011), 1691-1700.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406373

Digital Object Identifier
doi:10.11650/twjm/1500406373

Mathematical Reviews number (MathSciNet)
MR2848983

Zentralblatt MATH identifier
1234.26003

Subjects
Primary: 26A06: One-variable calculus
Secondary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15] 26A42: Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX]

Keywords
total H$_{1}$-integrability the fundamental theorem of calculus

Citation

Sarić, Branko. On Totalization of the $H_1$-Integral. Taiwanese J. Math. 15 (2011), no. 4, 1691--1700. doi:10.11650/twjm/1500406373. https://projecteuclid.org/euclid.twjm/1500406373


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