The Lévy radius of a set of probability measures satisfying basic moment conditions involving \(\{t,t^ 2\}\)
type: Item
instance of: scholarly article
title: The Lévy radius of a set of probability measures satisfying basic moment conditions involving \(\{t,t^ 2\}\)
zbMATH Open document ID: 0627.60024
DOI: 10.1007/BF01890569
published in: Constructive Approximation
publication date: 1987-01-01T00:00:00Z
review text: Let \(M(\epsilon_ 1,\epsilon_ 2)\) be the set of probability measures \(\mu\) satisfying \(| \int t^ jd\mu -s^ j_ 0| \leq \epsilon_ j\) for \(j=1,2\) with a real number \(s_ 0\). The author calculates the precise upper bound for the Lévy distance \(d_ L(\mu,\delta)\) between measures \(\mu\) in \(M(\epsilon_ 1,\epsilon_ 2)\) and the Dirac measure \(\delta\) concentrated at the point \(s_ 0\). The problem was motivated by \textit{P. P. Korovkin}'s theorem [Linear Operators and approximation theory. (1959; Zbl 0094.102), p. 6].
reviewed by: Rudolf Wegmann
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A44
zbMATH DE Number: 4020092
zbMATH Keywords: Lévy distance
zbMATH Keywords: Korovkin's theorem
author: George A. Anastassiou
MaRDI profile type: Publication
cites work: Q4183968
cites work: The General Moment Problem, A Geometric Approach
cites work: Q3272104
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description: scientific article; zbMATH DE number 4020092