The doubling metric and doubling measures
نویسندگان
چکیده
منابع مشابه
On fractional calculus associated to doubling and non-doubling measures
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We establish that there are bounded Jordan domains Ω ⊂ R (n ≥ 2) that do not carry a (nontrivial) doubling measure with respect to the Euclidean distance. More generally, it is shown that every nonempty metric space (X, d) without isolated points has an open and dense subset A such that (A, d) does not carry a doubling measure.
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It is known that in low dimensions supports of Hölder doubling measures are C1,β manifolds. In higher dimensions singularities may occur. We provide a full description of such supports by showing that they are C1,β manifolds away from a closed set of measure zero and that at singular points they are uniformly far from being flat at every scale.
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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 2020
ISSN: 0004-2080,1871-2487
DOI: 10.4310/arkiv.2020.v58.n2.a2