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arXiv · 1605.05596

The Stein Strömberg Covering Theorem in metric spaces

J. M. Aldaz
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Abstract

In \cite{NaTa} Naor and Tao extended to the metric setting the $O(d \log d)$ bounds given by Stein and Strömberg for Lebesgue measure in $\mathbb{R}^d$, deriving these bounds first from a localization result, and second, from a random Vitali lemma. Here we show that the Stein-Strömberg original argument can also be adapted to the metric setting, giving a third proof. We also weaken the hypotheses, and additionally, we sharpen the estimates for Lebesgue measure.

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J. M. Aldaz. 2017-01-07. The Stein Strömberg Covering Theorem in metric spaces. https://arxiv.org/abs/1605.05596

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