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Recent work of Fili and the author examines an ultrametric version of theMahler measure, denoted $M_\infty(\alpha)$ for an algebraic number $\alpha$. Weshow that the computation of $M_\infty(\alpha)$ can be reduced to a certainsearch through a finite set. Although it is a open problem to record the pointsof this set in general, we provide some examples where it is reasonable tocompute and our result can be used to determine $M_\infty(\alpha)$.

The finiteness of computing the ultrametric Mahler measure