N-Lusin property in metric measure spaces: A new sufficient condition

被引：1

作者：

Garriga, Marcela ^{[1
]}

Ochoa, Pablo ^{[2
]}

机构：

[1] Univ Nacl Cuyo, RA-5500 Mendoza, Argentina

[2] Univ Nacl Cuyo, CONICET, RA-5500 Mendoza, Argentina

来源：

FORUM MATHEMATICUM | 2018年 / 30卷 / 06期

关键词：

Abstract differentiation theory; area formula; N-Lusin condition; metric measure spaces; DIFFERENTIABILITY; MAPPINGS;

D O I：

10.1515/forum-2018-0016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we are concerned with the study of the N-Lusin property in metric measure spaces. A map satisfies that property if sets of measure zero are mapped to sets of measure zero. We prove a new sufficient condition for the N-Lusin property using a weak and pointwise Lipschitz-type estimate. Relations with approximate differentiability in metric measure spaces and other sufficient conditions for the N-Lusin property will be provided.

引用

页码：1475 / 1486

页数：12

共 50 条

[1] Equivalent Condition of the Measure Shadowing Property on Metric Spaces
Miao, Jie
Yang, Yinong
[J]. MATHEMATICS, 2024, 12 (06)
[2] On the measure contraction property of metric measure spaces
Ohta, Shin-ichi
[J]. COMMENTARII MATHEMATICI HELVETICI, 2007, 82 (04) : 805 - 828
[3] N-1-PROPERTY OF MAPPINGS AND LUSIN CONDITION (N)
PONOMAREV, SP
[J]. DOKLADY AKADEMII NAUK SSSR, 1988, 300 (02): : 288 - 290
[4] Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces
David, Guy C.
[J]. ANALYSIS AND GEOMETRY IN METRIC SPACES, 2015, 3 (01): : 296 - 312
[5] On the Bakry-Emery Condition, the Gradient Estimates and the Local-to-Global Property of RCD*(K, N) Metric Measure Spaces
Ambrosio, Luigi
Mondino, Andrea
Savare, Giuseppe
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2016, 26 (01) : 24 - 56
[6] Boundedness of Lusin-area and gλ* functions on localized BMO spaces over doubling metric measure spaces
Lin, Haibo
Nakai, Eiichi
Yang, Dachun
[J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2011, 135 (01): : 59 - 88
[7] A curvature-dimension condition for metric measure spaces
Sturm, KT
[J]. COMPTES RENDUS MATHEMATIQUE, 2006, 342 (03) : 197 - 200
[8] A UNIQUENESS PROPERTY FOR ANALYTIC FUNCTIONS ON METRIC MEASURE SPACES
Lysik, Grzegorz
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 148 (04) : 1679 - 1688
[9] A Sufficient Condition to a Regular Set Being of Positive Measure on Spaces
Kitabeppu, Yu
[J]. POTENTIAL ANALYSIS, 2019, 51 (02) : 179 - 196
[10] A Sufficient Condition to a Regular Set Being of Positive Measure on Spaces
Yu Kitabeppu
[J]. Potential Analysis, 2019, 51 : 179 - 196

← 1 2 3 4 5 →