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

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