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Zbl 0598.28010
Vol'berg, A.L.; Konyagin, S.V.
There is a homogeneous measure on any compact subset in $R\sp n$. (English. Russian original)
[J] Sov. Math., Dokl. 30, 453-456 (1984); translation from Dokl. Akad. Nauk SSSR 278, 783-786 (1984). ISSN 0197-6788

We prove that there is a nontrivial measure satisfying the doubling condition on any nonempty closed subset of ${\bbfR}\sp n$. The result is generalized to metric spaces, and the metric spaces carrying such measures are completely described.

MSC 2000:: *28A35 Measures and integrals in product spaces
28C15 Set functions and measures on topological spaces
42B25 Maximal functions
42B30 Hp-spaces (Fourier analysis)

Keywords: positive Borel measure; homogeneous measure; measure satisfying the doubling condition; metric spaces carrying such measures

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