  The Bernstein Markov Property, shortly BMP, is an asymptotic quan- titative
assumption on the growth of uniform norms of polynomials or rational functions
on a compact set with respect to L {\mu} 2 -norms, where {\mu} is a positive
finite measure. We consider two variants of BMP for rational functions with
restricted poles and compare them with the polynomial BMP finding out some
sufficient condi- tions for the latter to imply the former. Moreover, we
recover a sufficient mass- density condition for a measure to satisfy the
rational BMP on its support.
