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