Average approximations and moments of measures
type: Item
instance of: scholarly article
title: Average approximations and moments of measures
zbMATH Open document ID: 0953.41015
published in: Journal of Complexity
publication date: 2001-01-30T00:00:00Z
review text: Here the author investigates average approximation of infinite dimensional mappings and related problems connected with moments of measures. He constructs an example relating to unsolvability of approximation on the average of the identity mapping that confirms a conjecture of \textit{J. F. Traub} and \textit{A. G. Werschulz} [Math. Intell. 16, No. 2, 42-48 (1994; Zbl 0832.47010)]. Several positive results concerning average approximations of Banach space valued mappings are also obtained and some related existing results are improved upon.
Mathematics Subject Classification ID: 41A35
Mathematics Subject Classification ID: 46G12
Mathematics Subject Classification ID: 28C20
zbMATH DE Number: 1496869
zbMATH Keywords: Gauss measure
zbMATH Keywords: moments of measures
zbMATH Keywords: non-adaptive operator
zbMATH Keywords: information operator
zbMATH Keywords: average approximations
author: Vladimir I. Bogachev
reviewed by: Ganesh Datta Dikshit
MaRDI profile type: Publication
full work available at URL: jcom.2000.0541
OpenAlex ID: W1998084965
cites work: Locally convex spaces with the property of central limit theorem and measure supports
cites work: On the small balls problem for equivalent Gaussian measures
cites work: Convex measures on locally convex spaces
cites work: Gaussian radon measures on locally convex spaces.
cites work: Supports of Probability Measures in Separable Banach Spaces
cites work: Measurable norms and some Banach space valued Gaussian processes
cites work: Geometry of Banach spaces. Selected topics
cites work: Probabilistic complexity analysis for linear problems in bounded domains
cites work: Q4164570
cites work: Some results of probability measures on linear topological vector spaces with an application to Strassen's log log law
cites work: Q3997990
cites work: s-numbers in information-based complexity
cites work: Q4113166
cites work: Q5613420
cites work: Q4052400
cites work: Q3920145
cites work: Q3333786
cites work: Q3993279
cites work: Linear ill-posed problems are solvable on the average for all Gaussian measures
cites work: Q4040351
cites work: Renorming a Banach space to make a given subspace Chebyshev
cites work: Optimal algorithms for linear problems with Gaussian measures
cites work: Can adaption help on the average?
cites work: What is the complexity of ill-posed problems?
cites work: Q4000361
DOI: 10.1006/JCOM.2000.0541
description: scientific article; zbMATH DE number 1496869