  We show that the Korenblum maximum (domination) principle is valid for
weighted Bergman spaces $A^p_w$ with arbitrary (non-negative and integrable)
radial weights $w$ in the case $1\le p<\infty$. We also notice that in every
weighted Bergman space the supremum of all radii for which the principle holds
is strictly smaller than one. Under the mild additional assumption
$\liminf_{r\to 0^+} w(r)>0$, we show that the principle fails whenever $0<p<1$.
