Definition 18.28.43.48A0DBADBA86 Let $(K,v)$ be a weighted subset of $X$. A Borel probability measure $\mu $ on $K$ is Bernstein–Markov with respect to $(K,v)$ if for each $\epsilon >0$, there is a constant $C_\epsilon >0$ such that
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\begin{equation} N^ k_{v,K}(s) \leq C_\epsilon \mathrm{e}^{\epsilon k} N^ k_{v,\mu }(s) \end{equation}
for any $s \in \mathrm{H}^0(X,L^ k \otimes T)$ and any $k\in \mathbb {Z}_{>0}$. We write $\mathrm{BM}(K,v)$ for the set of Bernstein–Markov measures with respect to $(K,v)$.
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