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Based on Bohr's equivalence relation which was established for generalDirichlet series, in this paper we introduce a new equivalence relation on thespace of almost periodic functions in the sense of Besicovitch,$B(\mathbb{R},\mathbb{C})$, defined in terms of polynomial approximations. Fromthis, we show that in an important subspace $B^2(\mathbb{R},\mathbb{C})\subsetB(\mathbb{R},\mathbb{C})$, where Parseval's equality and Riesz-Fischer theoremholds, its equivalence classes are sequentially compact and the family oftranslates of a function belonging to this subspace is dense in its own class.

Bohr's equivalence relation in the space of Besicovitch almost periodic functions