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Given a compact set , for each positive integer n, let
= := sup: p holomorphic polynomial, 1 ≤ deg p ≤ n.
These “extremal-like” functions are essentially one-variable in nature and always increase to the “true” several-variable (Siciak) extremal function,
:= max[0, sup1/(deg p) log|p(z)|: p holomorphic polynomial, ].
Our main result is that if K is regular, then all of the functions are continuous; and their associated Robin functions
increase to for all z outside a pluripolar set....
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