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The doubling metric and doubling measures

János Flesch Department of Quantitative Economics, Maastricht University, The Netherlands Arkadi Predtetchinski Department of Economics, Maastricht University, The Netherlands Ville Suomala Department of Mathematical Sciences, University of Oulu, Finland

Algebraic Topology and General Topology mathscidoc:2203.44002

Arkiv for Matematik, 58, (2), 2020.11
We introduce the so-called doubling metric on the collection of non-empty bounded open subsets of a metric space. Given an open subset U of a metric space X, the predecessor U_∗ of U is defined by doubling the radii of all open balls contained inside U, and taking their union. The predecessor of U is an open set containing U. The directed doubling distance between U and another subset V is the number of times that the predecessor operation needs to be applied to U to obtain a set that contains V. Finally, the doubling distance between open sets U and V is the maximum of the directed distance between U and V and the directed distance between V and U.
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@inproceedings{jános2020the,
  title={The doubling metric and doubling measures},
  author={János Flesch, Arkadi Predtetchinski, and Ville Suomala},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311095107603968942},
  booktitle={Arkiv for Matematik},
  volume={58},
  number={2},
  year={2020},
}
János Flesch, Arkadi Predtetchinski, and Ville Suomala. The doubling metric and doubling measures. 2020. Vol. 58. In Arkiv for Matematik. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311095107603968942.
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