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.
B. Jessen (1948)
Colloquium Mathematicae
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Vladimír Rogalewicz (1984)
Časopis pro pěstování matematiky
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Schaerf, H.M. (1949)
Portugaliae mathematica
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Ricardo Faro Rivas, Juan A. Navarro, Juan Sancho (1994)
Extracta Mathematicae
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Ethan Akin, Randall Dougherty, R. Daniel Mauldin, Andrew Yingst (2008)
Colloquium Mathematicae
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For measures on a Cantor space, the demand that the measure be "good" is a useful homogeneity condition. We examine the question of when a Bernoulli measure on the sequence space for an alphabet of size n is good. Complete answers are given for the n = 2 cases and the rational cases. Partial results are obtained for the general cases.
Antonio Martinón (1989)
Extracta Mathematicae
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Stephen M. Buckley, Paul MacManus (2000)
Publicacions Matemàtiques
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We construct a sequence of doubling measures, whose doubling constants tend to 1, all for which kill a G set of full Lebesgue measure.
Stephen Bruce Sontz (2010)
Banach Center Publications
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This note explains how the two measures used to define the μ-deformed Segal-Bargmann space are natural and essentially unique structures. As is well known, the density with respect to Lebesgue measure of each of these measures involves a Macdonald function. Our primary result is that these densities are the solution of a system of ordinary differential equations which is naturally associated with this theory. We then solve this system and find the known densities as well as a "spurious"...
Igor Kluvánek (1977)
Annales de l'institut Fourier
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Every conical measure on a weak complete space is represented as integration with respect to a -additive measure on the cylindrical -algebra in . The connection between conical measures on and -valued measures gives then some sufficient conditions for the representing measure to be finite.
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...