Outer Minkowski content for some classes of closed sets
Outer Minkowski content for some classes of closed sets
复制标题
DOI：
10.1007/s00208-008-0254-z
复制
发表时间：
2008-06
影响因子：
1.4
通讯作者：
L. Ambrosio;A. Colesanti;E. Villa
中科院分区：
文献类型：
--
作者：
L. Ambrosio;A. Colesanti;E. Villa
我们找到了确保外闵可夫斯基内容福特维闭集存在的条件，与其边界的正则性质有关。此外，我们提供了一类在存在外部 Minkowski 内容的有限并下稳定的集合（包括所有足够规则的集合）。特别是，具有 Lipschitz 边界的集合的有限并和具有正到达的集合类型属于此类。
We find conditions ensuring the existence of theouter Minkowski contentford-dimensional closed sets in, in connection with regularity properties of their boundaries. Moreover, we provide a class of sets (including all sufficiently regular sets) stable under finite unions for which the outer Minkowski content exists. It follows, in particular, that finite unions of sets with Lipschitz boundary and a type of sets with positive reach belong to this class.