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.

Barbarino, G., Bianchi, D., Garoni, C. (2022). Constructive approach to the monotone rearrangement of functions. EXPOSITIONES MATHEMATICAE, 40(1), 155-175 [10.1016/j.exmath.2021.10.004].

### Constructive approach to the monotone rearrangement of functions

#### Abstract

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.
##### Scheda breve Scheda completa Scheda completa (DC)
2022
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05
English
Almost everywhere continuous functions
Asymptotically uniform grids and quasi-uniform samples
Generalized inverse distribution function
Monotone rearrangement
Quantile function
Uniform convergence
Barbarino, G., Bianchi, D., Garoni, C. (2022). Constructive approach to the monotone rearrangement of functions. EXPOSITIONES MATHEMATICAE, 40(1), 155-175 [10.1016/j.exmath.2021.10.004].
Barbarino, G; Bianchi, D; Garoni, C
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2108/297693`
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