标题： 各向异性Minkowski内容的存在性 显示英文标题

标题： Existence of Anisotropic Minkowski Content

摘要： 本文致力于各向异性Minkowski内容和各向异性外Minkowski内容的存在性。我们的结果是，给定有限周长的集合$E$的拓扑边界上的Minkowski内容与$E$的周长相等，当且仅当集合$E$的拓扑边界上的各向异性Minkowski内容与$E$的各向异性周长和$E.$补集的各向异性周长之和的一半相等。作为推论，我们发现给定有限周长的集合及其补集的各向异性外Minkowski内容的存在性保证了该集合及其补集的外Minkowski内容的存在性。 显示英文摘要

摘要： This paper is devoted to the existence of anisotropic Minkowski content and anisotropic outer Minkowski content. Our result is that the Minkowski content of the topological boundary of a given set of finite perimeter $E$ coincides with the perimeter of $E$ if and only if the anisotropic Minkowski content of the topological boundary of $E$ coincides with half of the sum of the anisotropic perimeter of $E$ and the anisotropic perimeter of the complement of $E.$ As a consequence, we find that the existence of anisotropic outer Minkowski content of a given set of finite perimeter and its complement ensures the existence of outer Minkowski content of the set and its complement.