### On a residue of complex functions in the three-dimensional Euclidean complex vector space.

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Let $[a,b]$ be an interval in $\mathbb{R}$ and let $F$ be a real valued function defined at the endpoints of $[a,b]$ and with a certain number of discontinuities within $[a,b]$. Assuming $F$ to be differentiable on a set $[a,b]\setminus E$ to the derivative $f$, where $E$ is a subset of $[a,b]$ at whose points $F$ can take values $\pm \infty $ or not be defined at all, we adopt the convention that $F$ and $f$ are equal to $0$ at all points of $E$ and show that $\mathrm{\mathcal{K}\mathscr{H}}\text{-vt}{\int}_{a}^{b}f=F\left(b\right)-F\left(a\right)$, where $\mathrm{\mathcal{K}\mathscr{H}}\text{-vt}$ denotes the total value of the integral. The paper ends with a few examples that illustrate the theory.

In this paper a full totalization is presented of the Kurzweil-Henstock integral in the multidimensional space. A residual function of the total Kurzweil-Henstock primitive is defined.

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