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.
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