A sufficient condition to a regular set of positive measure on RCD spaces
Metric Geometry
2017-08-16 v1
Abstract
In this paper, we study regular sets in metric measure spaces with bounded Ricci curvature. 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 thee dimension of metric measure spaces and prove the lower semicontinuity of that under the Gromov-Hausdorff convergence.
Keywords
Cite
@article{arxiv.1708.04309,
title = {A sufficient condition to a regular set of positive measure on RCD spaces},
author = {Yu Kitabeppu},
journal= {arXiv preprint arXiv:1708.04309},
year = {2017}
}
Comments
15 pages.arXiv admin note: text overlap with arXiv:1603.04162