It is proved that the filter dimenion is Morita invariant. A direct consequence of this fact is the Morita invariance of the inequality of Bernstein: if an algebra A is Morita equivalent to the ring D(X) of differential operators on a smooth irreducible affine algebraic variety X of dimension n ≥ 1 over a field of characteristic zero then the Gelfand-Kirillov dimension GK (M ) ≥ n = GK (A) 2 for all nonzero finitely generated A-modules M . In fact, a more strong result is proved, namely, a Morita invariance of the holonomic number for finitely generated algebra. As a direct consequence of this fact an affirmative answer is given to the question/conjecture posed by Ken Brown several years ago of whether an analogue of the inequality of Bernstein holds for the (simple) rational Cherednik algebras H c for integral c: GK (M ) ≥ n = GK (Hc) 2 for all nonzero finitely generated H c -modules M .