The doubling metric and doubling measures
| Autor: | János Flesch, Arkadi Predtetchinski, Ville Suomala |
|---|---|
| Přispěvatelé: | QE Math. Economics & Game Theory, RS: GSBE Theme Conflict & Cooperation, RS: FSE DACS Mathematics Centre Maastricht, Microeconomics & Public Economics |
| Rok vydání: | 2020 |
| Předmět: |
Primary 54E35
Secondary 28A12 51F99 metric General Mathematics General Topology (math.GN) Open set Metric Geometry (math.MG) 54E35 quasisymmetric map Combinatorics 51F99 Metric space Mathematics - Metric Geometry Mathematics - Classical Analysis and ODEs Bounded function doubling measure Metric (mathematics) Classical Analysis and ODEs (math.CA) FOS: Mathematics 28A12 Quasisymmetric map Mathematics - General Topology Mathematics |
| Zdroj: | Ark. Mat. 58, no. 2 (2020), 243-266 Arkiv for Matematik, 58(2), 243-266. Springer |
| ISSN: | 1871-2487 0004-2080 |
| DOI: | 10.4310/arkiv.2020.v58.n2.a2 |
| Popis: | We introduce the so--called doubling metric on the collection of non--empty bounded open subsets of a metric space. Given a 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. If $U$ is open, 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 $U$ and $V$ is the maximum of the directed distance between $U$ and $V$ and the directed distance between $V$ and $U$. Comment: 22 pages |
| Databáze: | OpenAIRE |
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