度量空间中的Stein Strömberg覆盖定理
The Stein Strömberg Covering Theorem in metric spaces
摘要：
在\cite{NaTa} Naor和陶扩展到度量设置的$O(d \log d)$界限由斯坦和Strömberg的勒贝格测度在$\mathbb{R}^d$，这些界限首先从本地化的结果，第二，从一个随机维塔利引理。在这里，我们表明，斯坦-斯特伦伯格原来的论点也可以适应的度量设置，给第三个证明。我们也削弱了假设，此外，我们锐化的估计勒贝格测度。
英文摘要：
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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