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Some Measure-Theoretic Properties of Packing Measure

Periodica Mathematica Hungarica, 1998
This paper is an informal discussion of some fundamental measure-theoretic differences between the families of measures known as packing measures and Hausdorff measures. Two main issues of focus are, whether or not a set of infinite measure necessarily contains a subset of positive finite measure, and the question of Borel regularity.
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Measuring Corner Properties

Computer Vision and Image Understanding, 1999
We describe methods to measure the following properties of gray level corners: subtended angle, orientation, contrast, bluntness (or rounding of the apex), and boundary curvature (for cusps). Unlike most of the published methods for extracting these properties these new methods are relatively simple, efficient, and robust. They rely on the corner being
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Tail Properties of Correlation Measures

Journal of Theoretical Probability, 2003
The authors study the tail properties of a class of Borel probability measures, called correlation measures. They show that (1) there exist correlation measures with exponentially decaying tail probabilities, and (2) roughly speaking, no correlation measure may have smaller tail probabilities than a Gaussian measure.
Lewis, Thomas M., Pritchard, Geoffrey
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Density Properties of Harmonic Measure

The Annals of Mathematics, 1995
Some metric properties of harmonic measure are studied in the paper. The basis of all considerations is the known formula \(f(x)= \int_{\partial \Omega} u dw_z\) which solves the Dirichlet problem \(\Delta f=0\) on \(\Omega \subset \mathbb{R}^n\), \(f=u\) on \(\partial \Omega\) and \(w_z\) a Borel probability measure on \(\partial \Omega\).
Jones, P. W., Makarov, Nikolai G.
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Measurability Properties of Mazurkiewicz Sets

2022
Summary: We consider the family of Mazurkiewicz subsets of the Euclidean plane from the measure-theoretical point of view. In particular, it is shown that all Mazurkiewicz sets are negligible and there exists a Mazurkiewicz set which is absolutely negligible.
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