The aim of this paper is to study Sp remotely almost periodic (Stepanov remotely almost periodic) functions defined on \({\mathbb T}\in \{{\mathbb R},{\mathbb R}_{+}\}\) with values in the Banach space \(\frak{B}\) . We establish a relation between remotely almost periodic motions in the shift dynamical system \((L^{p}_{\rm{loc}}({\mathbb T},{\frak B}),{\mathbb T},\sigma)\) and Sp remotely almost periodic functions in the space of locally measurable functions \(L^{p}_{\rm{loc}}({\mathbb T},{\frak B})\) . Using this relation, we establish some important algebraic, analytical and topological properties of Sp almost periodic functions.
