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Títol:	A characterization of 1-rectifiable doubling measures with connected supports
Autor/a:	Azzam, J.; Mourgoglou, M.
Abstract:	Garnett, Killip, and Schul have exhibited a doubling measure μ with support equal to Rd that is 1- rectifiable, meaning there are countably many curves Γi of finite length for which μ(Rd\υΓi) = 0. In this note, we characterize when a doubling measure μ with support equal to a connected metric space X has a 1-rectifiable subset of positive measure and show this set coincides up to a set of μ-measure zero with the set of x ∈ X for which lim infr→0 μ(BX (x, r))/r > 0.
Data de publicació:	01-01-2016
Matèries:	51
Pàgines:	14 p.
Tipus de document:	Article Article - Versió publicada
DOI:	10.2140/apde.2016.9.99
Publicat per:	Mathematical Sciences Publishers
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