关于度量空间上Lipschitz函数剩余子集的注记
A note on a residual subset of Lipschitz functions on metric spaces
摘要：
设（X，d）是具有参考概率测度m的拟凸完备可分度量空间.证明了在Lipschitz和有界函数的巴拿赫空间中，具有非零点Lipschitz常数m-几乎处处的实值Lipschitz函数的集合是剩余的，因而是稠密的.这个结果是Alberti，Bianchini和Crippa在[1]中对定义在R2上的实值Lipschitz映射所证明的一个结果的度量类似。
英文摘要：
Let (X, d) be a quasi-convex, complete and separable metric space with reference probability measure m. We prove that the set of of real valued Lipschitz function with non zero point-wise Lipschitz constant m-almost everywhere is residual, and hence dense, in the Banach space of Lipschitz and bounded functions. The result is the metric analogous of a result proved for real valued Lipschitz maps defined on R2 by Alberti, Bianchini and Crippa in [1].
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