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On the Rate of Convergence of \(\big (\frac{\Vert f\Vert _{p}}{\Vert f\Vert _{\infty }}\big )^{p}\) as \(p\rightarrow \infty \)

  • L. OlsenEmail author
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Abstract

Let \((X,{\mathcal {E}},\mu )\) be a measure space and let \(f:X\rightarrow \mathbb R\) be a measurable function such that \(\Vert f\Vert _{p}<\infty \) for all \(p\ge 1\) and \(\Vert f\Vert _{\infty }>0\). In this paper, we describe the rate of convergence of \((\frac{\Vert f\Vert _{p}}{\Vert f\Vert _{\infty }})^{p}\) as \(p\rightarrow \infty \).

Keywords

\(L^{p}\)-norm rate of convergence 

Mathematics Subject Classification

28A10 28A20 

Notes

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Copyright information

© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of St. AndrewsSt. AndrewsScotland, UK

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