The Symmetric Decreasing Rearrangement Via the Bubble Sort

Abstract

We define a constructive method of 'approximately sorting' a non-negative continuous function $f$ on $\mathbb{R}^n$. Specifically the symmetric decreasing rearrangement $f^*$ can be considered the sorted version of $f$ and certain equimeasurable rearrangements of $f$ are then sorted and shown to converge uniformly to $f^*$.