= Modulus powers of holomorphic functions are subharmonic
{title2=$\Delta|f|^p=p^2|f|^{p-2}|f'|^2\ge0\quad(f\ne0,\ p>0)$}
For every <holomorphic function> and $p>0$, $|f|^p$ is <subharmonic>. Away from its zeros the displayed <Laplacian> calculation proves this. At the zeros, use the smooth approximations $(|f|^2+\varepsilon)^{p/2}$, whose <Laplacians> are nonnegative, and let $\varepsilon\downarrow0$ in their mean inequalities. This permits <Poisson integral> comparison for fractional modulus powers even when a global analytic fractional power does not exist.
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