度量空间中测度的微分
Differentiation of measures in metric spaces
摘要：
测度微分理论起源于贝西科维奇20世纪40年代的著作。他的开创性工作，以及随后的理论发展，依赖于适当的覆盖性质作为基本工具。这些说明的第一个目的是回顾当今经典的结果分化的措施在度量设置连同覆盖性质的基础上。然后，我们将重点放在这些覆盖性质之一，在本说明中称为弱贝西科维奇覆盖性质，它在（完全可分）度量空间的特征中起着核心作用，其中微分定理对每个（局部有限Borel正则）测度都成立。我们在这些笔记的最后一部分审查最近的结果有效性或无效性的覆盖性质。
英文摘要：
The theory of differentiation of measures originates from works of Besicovitch in the 1940's. His pioneering works, as well as subsequent developments of the theory, rely as fundamental tools on suitable covering properties. The first aim of these notes is to recall nowadays classical results about differentiation of measures in the metric setting together with the covering properties on which they are based. We will then focus on one of these covering properties, called in the present notes the weak Besicovitch covering property, which plays a central role in the characterization of (complete separable) metric spaces where the differentiation theorem holds for every (locally finite Borel regular) measure. We review in the last part of these notes recent results about the validity or non validity of this covering property.
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