Constructive approach to the monotone rearrangement of functions

Giovanni Barbarino, Davide Bianchi, Carlo Garoni*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)155-175
Number of pages21
JournalExpositiones Mathematicae
Issue number1
Early online date2021
Publication statusPublished - 2022
MoE publication typeA1 Journal article-refereed


  • Almost everywhere continuous functions
  • Asymptotically uniform grids and quasi-uniform samples
  • Generalized inverse distribution function
  • Monotone rearrangement
  • Quantile function
  • Uniform convergence


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