Discretization and best approximation in Besov spaces

In this paper we prove a theorem about existence of best approximation in a class of spaces involving Besov spaces, via a discretization technique. It is a consequence of this theorem that rational functions and exponencial sums are proximinal subsets of B _∞,q ^a (π). It is also proved the proximinality of R _m ⁿ a, b] in B _p,q ^a (π) for arbitrary p,q and a.