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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Monotone $L_ 1$-approximation on the unit $n$-cube


Authors: Richard B. Darst and Robert Huotari
Journal: Proc. Amer. Math. Soc. 95 (1985), 425-428
MSC: Primary 41A52; Secondary 41A29
DOI: https://doi.org/10.1090/S0002-9939-1985-0806081-7
MathSciNet review: 806081
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Abstract: Let $\Omega$ be the unit $n$-cube ${[0,1]^n}$, and let $M$ be the set of all real-valued functions on $\Omega$, each of which is nondecreasing in each variable separately. If $f:\Omega \to \mathbb {R}$ is continuous, we show that there exists an (essentially) unique, best ${L_1}$-approximation, ${f_1}$, to $f$ by elements of $M$, and that ${f_1}$ is continuous.


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Article copyright: © Copyright 1985 American Mathematical Society