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FEDERER'S CHARACTERIZATION OF SETS OF FINITE PERIMETER IN METRIC SPACES
Lahti, Panu
2020
Source PublicationANALYSIS & PDE
ISSN1948-206X
Volume13Issue:5Pages:1501-1519
AbstractFederer's characterization of sets of finite perimeter states (in Euclidean spaces) that a set is of finite perimeter if and only if the measure-theoretic boundary of the set has finite Hausdorff measure of codimension 1. In complete metric spaces that are equipped with a doubling measure and support a Poincare inequality, the "only if" direction was shown by Ambrosio (2002). By applying fine potential theory in the case p = 1, we prove that the "if" direction holds as well.
Keywordmetric measure space set of finite perimeter Federer's characterization measure-theoretic boundary codimension-1 Hausdorff measure fine topology
DOI10.2140/apde.2020.13.1501
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000555886800007
PublisherMATHEMATICAL SCIENCE PUBL
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/51968
Collection应用数学研究所
Corresponding AuthorLahti, Panu
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Lahti, Panu. FEDERER'S CHARACTERIZATION OF SETS OF FINITE PERIMETER IN METRIC SPACES[J]. ANALYSIS & PDE,2020,13(5):1501-1519.
APA Lahti, Panu.(2020).FEDERER'S CHARACTERIZATION OF SETS OF FINITE PERIMETER IN METRIC SPACES.ANALYSIS & PDE,13(5),1501-1519.
MLA Lahti, Panu."FEDERER'S CHARACTERIZATION OF SETS OF FINITE PERIMETER IN METRIC SPACES".ANALYSIS & PDE 13.5(2020):1501-1519.
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