A Sufficient Condition to a Regular Set Being of Positive Measure on Spaces

被引：21

作者：

Kitabeppu, Yu ^{[1
]}

机构：

[1] Kumamoto Univ, Fac Adv Sci & Technol, Kumamoto 8608555, Japan

来源：

POTENTIAL ANALYSIS | 2019年 / 51卷 / 02期

关键词：

RCD spaces; Regular sets; METRIC MEASURE-SPACES; CURVATURE-DIMENSION CONDITION; RICCI CURVATURE; CONVERGENCE; INEQUALITY; CONTINUITY; FLOWS;

D O I：

10.1007/s11118-018-9708-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study regular sets in metric measure spaces with Ricci curvature bounded from below. We prove that the existence of a point in the regular set of the highest dimension implies the positivity of the measure of such regular set. Also we define the dimension of RCD spaces and prove the lower semicontinuity of that under the Gromov-Hausdorff convergence.

引用

页码：179 / 196

页数：18

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