Displaying similar documents to “How the μ-deformed Segal-Bargmann space gets two measures”

Research Article. Multiscale Analysis of 1-rectifiable Measures II: Characterizations

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...

Can interestingness measures be usefully visualized?

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...

Extending Coarse-Grained Measures

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...

On density theorems for outer measures

E. J. Mickle, T. Rado

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CONTENTSINTRODUCTION................................................................................... 3SECTION 1. Covering theorems........................................................... 5SECTION 2. Absolutely measurable sets.............................................. 8SECTION 3. Generalized spherical Hausdorff measures.................... 14SECTION 4. Density theorems for subadditive set functions............... 20SECTION 5. A density theorem for outer measures...............................

Fonction de Correlation pour des Mesures Complexes

Wei Min Wang (1998-1999)

Séminaire Équations aux dérivées partielles

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We study a class of holomorphic complex measures, which are close in an appropriate sense to a complex Gaussian. We show that these measures can be reduced to a product measure of real Gaussians with the aid of a maximum principle in the complex domain. The formulation of this problem has its origin in the study of a certain class of random Schrödinger operators, for which we show that the expectation value of the Green’s function decays exponentially.