度量测度空间上Cheeger导数的Lusin型定理
Lusin-type theorems for Cheeger derivatives on metric measure spaces
摘要：
Lusin的一个定理指出，$R$上的每一个Borel函数几乎处处等于一个连续函数的导数。这个结果后来在Alberti和Moonens-Pfeffer的著作中推广到了$R^n$。本文在一类度量测度空间上证明了这些结果的直接类似物，这些度量空间具有加倍测度和Poincaré不等式，它们通过Cheeger的一个著名定理允许一种形式的微分。
英文摘要：
A theorem of Lusin states that every Borel function on $R$ is equal almost everywhere to the derivative of a continuous function. This result was later generalized to $R^n$ in works of Alberti and Moonens-Pfeffer. In this note, we prove direct analogs of these results on a large class of metric measure spaces, those with doubling measures and Poincaré inequalities, which admit a form of differentiation by a famous theorem of Cheeger.
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