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

Springer Science and Business Media LLC - Tập 51 - Trang 179-196 - 2018
Yu Kitabeppu1
1Faculty of Advanced Science and Technology, Kumamoto University, Kumamoto, Japan

Tóm tắt

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.

Tài liệu tham khảo

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