Riemann Integral of Functions from R into n-dimensional Real Normed Space

Abstract

Summary. In this article, we define the Riemann integral on functions Rinto n-dimensional real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to the wider range. Our method refers to the [21].MML identifier: INTEGR19, version: 7.1 .0 4.1 .11The terminology and notation used in this paper have been introduced in the following papers: [23] On the Functions from R into n-dimensional Real SpaceFor simplicity, we adopt the following convention: X denotes a set, n denotes an element of N, a, b, c, d, e, r, x 0 denote real numbers, A denotes a non empty closed-interval subset of R, f , g, h denote partial functions from R to R n , and E denotes an element of R n . We now state a number of propositions:(

The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space

“…The notation and terminology used in this paper have been introduced in the following articles: [2], [12], [3], [4], [9], [10], [7], [8], [16], [1], [17], [13], [14], [5], [15], [20], [21], [18], [19], [22], and [6].…”