# Constructive approach to the monotone rearrangement of functions

Giovanni Barbarino, Davide Bianchi, Carlo Garoni*

*Tämän työn vastaava kirjoittaja

Tutkimustuotos: LehtiartikkeliArticleScientificvertaisarvioitu

2 Sitaatiot (Scopus)

## Abstrakti

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.

Alkuperäiskieli Englanti 155-175 21 Expositiones Mathematicae 40 1 2021 https://doi.org/10.1016/j.exmath.2021.10.004 Julkaistu - 2022 A1 Julkaistu artikkeli, soviteltu

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