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