= Radial logarithmic mean of a Blaschke product
{title2=$\int\log|B(r\xi)|\,dm=m\log r+\sum_n\log\max(r,|a_n|)$}
For $B(z)=\lambda z^m\prod_n b_{a_n}(z)$ with nonzero zeros $a_n$ counted with <multiplicity>, <Jensen's formula> gives the displayed identity. The negative logarithms of partial products increase, so the <monotone convergence theorem> permits termwise integration. The <Blaschke condition> implies $\sum_n-\log|a_n|<\infty$, which dominates the absolute summands. The <dominated convergence theorem> therefore gives a limit of zero as $r\uparrow1$. Since $|B|\le1$, the mean of $|\log|B||$ tends to zero as well.
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