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.
Ai Fan (1996)
Studia Mathematica
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We give a simple proof of the sufficiency of a log-lipschitzian condition for the uniqueness of G-measures and g-measures which were studied by G. Brown, A. H. Dooley and M. Keane. In the opposite direction, we show that the lipschitzian condition together with positivity is not sufficient. In the special case where the defining function depends only upon two coordinates, we find a necessary and sufficient condition. The special case of Riesz products is discussed and the Hausdorff dimension...
B. Jessen (1948)
Colloquium Mathematicae
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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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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.
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...
K. P. S. Bhaskara Rao, B. V. Rao (1979)
Colloquium Mathematicae
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Anna De Simone, Pavel Pták (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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In [4] it is proved that a measure on a finite coarse-grained space extends, as a signed measure, over the entire power algebra. In [7] this result is reproved and further improved. Both the articles [4] and [7] use the proof techniques of linear spaces (i.e. they use multiplication by real scalars). In this note we show that all the results cited above can be relatively easily obtained by the Horn-Tarski extension technique in a purely combinatorial manner. We also characterize the...
Barnes, Julia A., Eigen, Stanley J. (2000)
The New York Journal of Mathematics [electronic only]
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Robert Susmaga, Izabela Szczech (2015)
International Journal of Applied Mathematics and Computer Science
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The paper presents visualization techniques for interestingness measures. The process of measure visualization provides useful insights into different domain areas of the visualized measures and thus effectively assists their comprehension and selection for different knowledge discovery tasks. Assuming a common domain form of the visualized measures, a set of contingency tables, which consists of all possible tables having the same total number of observations, is constructed. These...
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.
Antonio Martinón (1989)
Extracta Mathematicae
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Alexander I. Bufetov (2014)
Annales de l’institut Fourier
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The main result of this note, Theorem 1.3, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant and ergodic under the action of the infinite unitary group and that admits well-defined projections onto the quotient space of “corners" of finite size, must be finite. A similar result, Theorem 1.1, is also established for unitarily invariant measures on the space of all infinite complex matrices. These results imply that the infinite Hua-Pickrell...