函数单调重排的构造性方法
Constructive approach to the monotone rearrangement of functions
摘要：
我们详细介绍了一个简单的程序（很容易转换成一个算法）从准均匀样本的$f$的线性样条函数序列收敛到单调重排的$f$，在这种情况下，$f$是一个几乎处处连续函数定义在一个有界集$Ω$可忽略的边界。在对$f$和$Ω$的附加假设下，证明了序列的一致收敛性.我们还表明，同样的程序适用于任意可测函数太，但与实质性的区别，在这种情况下，该程序只有理论上的利益，不能转换为一个算法。
英文摘要：
We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost everywhere continuous function defined on a bounded set $Ω$ with negligible boundary. Under additional assumptions on $f$ and $Ω$, we prove that the convergence of the sequence is uniform. We also show that the same procedure applies to arbitrary measurable functions too, but with the substantial difference that in this case the procedure has only a theoretical interest and cannot be converted to an algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
