Local Hausdorff Measure
Metric Geometry
2016-10-04 v1
Abstract
A local Hausdorff dimension is defined on a metric space. We study its properties and use it to define a local Hausdorff measure. We show that in the case that in the local Hausdorff measure is finite we can recover the global Hausdorff dimension from the local one. Lastly, for a variable Ahlfors Q-regular measure on a compact metric space, we show the Ahlfors regular measure is strongly equivalent to the local Hausdorff measure and that the function is equal to the local Hausdorff dimension.
Cite
@article{arxiv.1610.00078,
title = {Local Hausdorff Measure},
author = {John Dever},
journal= {arXiv preprint arXiv:1610.00078},
year = {2016}
}