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Proceedings of the American Mathematical Society

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

 
 

 

Monotone $ L\sb 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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DOI: https://doi.org/10.1090/S0002-9939-1985-0806081-7
Article copyright: © Copyright 1985 American Mathematical Society

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