Ralph E. Edwards (1958)
Annales de l'institut Fourier
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L’auteur détaille l’extension de la méthode de balayage de Cartan à des potentiels de Green, sur une surface de Riemann hyperbolique. Une extension des méthodes de balayage de Frostman, de la Vallée-Poursin, lui permet de démontrer que l’énergie de toute mesure est positive, puis d’obtenir l’extension en vue.
Matthew Badger, Raanan Schul (2017)
Analysis and Geometry in Metric Spaces
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A measure is 1-rectifiable if there is a countable union of finite length curves whose complement has zero measure. We characterize 1-rectifiable Radon measures μ in n-dimensional Euclidean space for all n ≥ 2 in terms of positivity of the lower density and finiteness of a geometric square function, which loosely speaking, records in an L2 gauge the extent to which μ admits approximate tangent lines, or has rapidly growing density ratios, along its support. In contrast with the classical...
Ricardo Faro Rivas, Juan A. Navarro, Juan Sancho (1994)
Extracta Mathematicae
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A. Ülger (2007)
Studia Mathematica
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Let G be a locally compact abelian group and M(G) its measure algebra. Two measures μ and λ are said to be equivalent if there exists an invertible measure ϖ such that ϖ*μ = λ. The main result of this note is the following: A measure μ is invertible iff |μ̂| ≥ ε on Ĝ for some ε > 0 and μ is equivalent to a measure λ of the form λ = a + θ, where a ∈ L¹(G) and θ ∈ M(G) is an idempotent measure.
Thiruvaiyaru V. Panchapagesan (1992)
Czechoslovak Mathematical Journal
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Astels, S. (1999)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Benoît Kloeckner (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the problem of approximating a probability measure defined on a metric space by a measure supported on a finite number of points. More specifically we seek the asymptotic behavior of the minimal Wasserstein distance to an approximation when the number of points goes to infinity. The main result gives an equivalent when the space is a Riemannian manifold and the approximated measure is absolutely continuous and compactly supported....
Benoît Kloeckner (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the problem of approximating a probability measure defined on a metric space by a measure supported on a finite number of points. More specifically we seek the asymptotic behavior of the minimal Wasserstein distance to an approximation when the number of points goes to infinity. The main result gives an equivalent when the space is a Riemannian manifold and the approximated measure is absolutely continuous and compactly supported....