The semicontinuity of dimensions of measures
Daiki Takagi
Abstract
In this paper, we consider certain uniformity conditions on the radii of balls. Under these conditions, we study the semicontinuity of the Hausdorff dimension of measures with respect to measured Gromov--Hausdorff convergence and box convergence. We also examine the semicontinuity of other dimensions of measures, which are similar to the Hausdorff dimension of measures.
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