  In this note we prove that if a sublinear operator T satisfies a certain
weighted estimate in the $L^{p}(w)$ space for all $w\in A_{p}$, $1<p<+\infty$,
then the operator norm of T on $L^{p}(w)$ is a continuous function of the
weight $w$, with respect to a certain metric $d_{*}$ on $A_{p}$. This,
generalizes a previous result on the same subject for linear operators.
