  We prove that certain sequences of Laurent polynomials, obtained from a fixed
Laurent polynomial P by monomial substitutions, give rise to sequences of
Mahler measures which converge to the Mahler measure of P. This generalizes
previous work of Boyd and Lawton, who considered univariate monomial
substitutions. We provide moreover an explicit upper bound for the error term
in this convergence, generalizing work of Dimitrov and Habegger, and a full
asymptotic expansion for a family of 2-variable polynomials, whose Mahler
measures were studied independently by the third author.
