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