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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Continuity of best approximants
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by D. Landers and L. Rogge PDF
Proc. Amer. Math. Soc. 83 (1981), 683-689 Request permission

Abstract:

Let ${C_n}$, $n \in {\mathbf {N}}$, be $\Phi$-closed lattices in an Orlicz-space ${L_\Phi }(\Omega , \mathcal {A}, \mu )$ and assume that ${C_n}$ increases or decreases to a $\Phi$-closed lattice ${C_\infty }$. Let ${f_n}$, $n \in {\mathbf {N}}$, be $\mathcal {A}$-measurable real valued functions with ${f_n} \to f\mu$-a.e. and $\sup |{f_n}| \in {L_\Phi }$. If ${g_n}$ is a best $\Phi$-approximant of ${f_n}$ in ${C_n}$ it is shown that ${\underline {\lim } _{n \in {\mathbf {N}}}}{g_n}$ and ${\overline {\lim } _{n \in {\mathbf {N}}}}{g_n}$ are best $\Phi$-approximants of $f$ in ${C_\infty }$.
References
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 83 (1981), 683-689
  • MSC: Primary 46E30; Secondary 41A65
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0630037-7
  • MathSciNet review: 630037