Ahlfors正则空间上的开集分解与加倍测度

The decomposition of open subsets in Ahlfors regular spaces and doubling measures

对于一致完全的加倍度量空间建立了Whitney分解定理.作为应用,借助于Ahlfors正则空间上的加倍测度描述了它的任意非空闭集的Whitney修正集上的加倍测度.

We prove that Whitney＇s decomposition theorem is true for any uniformly perfect doubling metric space. As an application, we describe doubling measures on the Whitney modification set of a nonempty closed subset in an Ahlfors regular space X, by means of doubling measures on X.