Constructive approach to the monotone rearrangement of functions

We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ sequence linear spline functions converging the monotone rearrangement $f$, in case where is almost everywhere continuous function defined on bounded set $\Omega$ with negligible boundary. Under additional assumptions and $\Omega$, we prove that convergence uniform. also show same applies arbitrary measurable too, but substantial difference this has only theoretical interest cannot be converted algorithm.