Adam Bowers (2010)
Studia Mathematica
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We relate the Grothendieck inequality to the theory of vector measures and show that the integral of an inner product with respect to a bimeasure can be computed in an iterative way. We then show an application to the theory of bounded linear operators.
V. R. Rakočević (1983)
Matematički Vesnik
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José García-Cuerva, A. Eduardo Gatto (2004)
Studia Mathematica
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The main purpose of this paper is to investigate the behavior of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed power of its radius. This allows, in particular, non-doubling measures. It turns out that this condition is enough to build up a theory that contains the classical results based upon the Lebesgue measure on Euclidean space and their known extensions...
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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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...
Heiming, Helmut J. (1996)
Abstract and Applied Analysis
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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.
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.
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...
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"...
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...
Wu, Jang-Mei (1993)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Dubtsov, E.S. (2004)
Zapiski Nauchnykh Seminarov POMI
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Schaerf, H.M. (1949)
Portugaliae mathematica
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