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Uniform measures on inverse limit spaces [PDF]
Applicable Analysis, 2009 Motivated by problems from dynamic economic models, we consider the problem of defining a uniform measure on inverse limit spaces. Let where X is a compact metric space and f is continuous, onto and piecewise one-to-one and . Then starting with a measure μ1 on the Borel sets , we recursively construct a sequence of probability measures on satisfying ...
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On Harmonic Measure and Rectifiability in Uniform Domains
The Journal of Geometric Analysis, 2018Let \(\omega \) denote harmonic measure for a domain \(\Omega \) in \(\mathbb{R}^{d+1}\), where \(d\geq 1\). There is an extensive literature investigating conditions on \(\partial \Omega \) which ensure that the \(d\)-dimensional Hausdorff measure \(\mathcal{H}^{d}|_{\partial \Omega }\) satisfies \(\mathcal{H}^{d}|_{\partial \Omega }\ll \omega \), or \
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2012
In this chapter I show how to obtain several familiar spaces of measures and measure-like functionals as \(\mathsf{{\mathfrak{M}}_{u}}(X)\) for suitably chosen uniform spaces X, and how to derive properties of spaces of measures from the results in Chap. 6.
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In this chapter I show how to obtain several familiar spaces of measures and measure-like functionals as \(\mathsf{{\mathfrak{M}}_{u}}(X)\) for suitably chosen uniform spaces X, and how to derive properties of spaces of measures from the results in Chap. 6.
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The Measure Spectrum of a Uniform Algebra and Subharmonicity
Canadian Journal of Mathematics, 1982Let A be a uniform algebra on a compact Hausdorff space X. The spectrum, or the maximal ideal space, MA, of A is given byWe define the measure spectrum, SA, of A bySA is the set of all representing measures on X for all Φ ∈ MA. (A representing measure for Φ ∈ MA is a probability measure μ on X satisfyingThe concept of representing measure continues to ...
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On uniform quantization with various distortion measures
IEEE Trans. Inf. Theory, 1987Upper bounds are presented for the difference in entropy between that of a uniform scalar quantizer and that of any N-dimensional quantizer. The bounds are universal in the sense that they suit every input density and every value of distortion. Bounds were found for some common distortion criteria.
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Uniform convergence of empirical and predictive measures
2002Uniform Convergence of Empirical and Predictive Measures.
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Uniform algebras and measures.
2015The purpose of this work is to demonstrate the vital role played by measures in the study of Uniform Algebras. Most authors in the subject of Uniform Algebras are, essentially, Functional Analysts and this emphasis is apparent in their treatment of the subject.
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Statistical measures of two dimensional point set uniformity
Computational Statistics and Data Analysis, 2012Ye Chow Kuang, Melanie Po-Leen Ooi
exaly