The Multiple K -Riemann Integral

Abstract

The aim of this paper is to extend the notion of $\mathbb{K}$ -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 $\mathbb{K}$ -step functions which allows us to give an equivalent definition of the $\mathbb{K}$ -Riemann integrable functions.