The Multiple 𝕂-Riemann Integral

Abstract

The aim of this paper is to extend the notion of $𝕂$-Riemann integrability of functions defined over $\left[a,b\right]$ to functions defined over a rectangular box of ${ℝ}^n$. As a generalization of step functions, we introduce a notion of $𝕂$-step functions which allows us to give an equivalent definition of the $𝕂$-Riemann integrable functions.