Approach to the construction of the spaces $S{D}^p[{\mathbb{R}}^{\infty }]$ for $1\le p\le \infty$

Abstract

The objective of this paper is to construct separable Banach spaces $S{D}^p[{\mathbb{R}}^{\infty }]$ for $1\le p\le \infty$, each of which contains the $L^p[{\mathbb{R}}^{\infty }]$ spaces, as well as finitely additive measures, as compact dense embedding. Also these spaces contains Henstock-Kurzweil integrable functions.

15, revised version