The size of the set of μ-irregular points of a measure μ

Eli Levin; Doron S. Lubinsky

doi:10.1007/s10474-011-0091-5

The size of the set of μ-irregular points of a measure μ

Eli Levin, Doron S. Lubinsky

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let μ be a compactly suppported positive measure on the real line. A point x∈supp [μ] is said to be μ-regular, if, as n → ∞, Otherwise it is a μ-irregular point. We show that for any such measure, the set of μ-irregular points in {μ′>0} (with a suitable definition of this set) has Hausdorff m_hβ measure 0, for h_β(t) = (log 1/t)^-β, any β>1.

Original language	English
Pages (from-to)	242-250
Number of pages	9
Journal	Acta Mathematica Hungarica
Volume	133
Issue number	3
DOIs	https://doi.org/10.1007/s10474-011-0091-5
State	Published - Nov 2011

Bibliographical note

Funding Information:
∗Corresponding author. †Research supported by NSF grant DMS1001182 and US-Israel BSF grant 2008399. Key words and phrases: orthogonal polynomial on the real line, regular measure, irregular point. 2000 Mathematics Subject Classification: 42C05, 42C99.

Keywords

irregular point
orthogonal polynomial on the real line
regular measure

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10.1007/s10474-011-0091-5

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AB - Let μ be a compactly suppported positive measure on the real line. A point x∈supp [μ] is said to be μ-regular, if, as n → ∞, Otherwise it is a μ-irregular point. We show that for any such measure, the set of μ-irregular points in {μ′>0} (with a suitable definition of this set) has Hausdorff mhβ measure 0, for hβ(t) = (log 1/t)-β, any β>1.

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The size of the set of μ-irregular points of a measure μ

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Keywords

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