Probabilistic norms and convergence of random variables
type: Item
instance of: scholarly article
title: Probabilistic norms and convergence of random variables
zbMATH Open document ID: 1020.60018
DOI: 10.1016/S0022-247X(02)00577-2
author: Bernardo Lafuerza Guillén
author: Carlo Sempi
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-05-25T00:00:00Z
review text: It is well-known that almost sure convergence is not metrizable. To circumvent this, the authors use the notion of probabilistic normed spaces, in particular Šerstnev spaces [see e.g. \textit{B. Schweizer} and \textit{A. Sklar}, ``Probabilistic metric spaces'' (1983; Zbl 0546.60010)] and construct a number of such spaces inducing different modes of convergence, as e.g., convergence in probability, \(L_p\)-convergence and almost sure convergence.
reviewed by: Ulrich Stadtmüller
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 28A20
Mathematics Subject Classification ID: 46S50
Mathematics Subject Classification ID: 60B99
zbMATH DE Number: 1915601
zbMATH Keywords: convergence in probability
zbMATH Keywords: almost sure convergence
zbMATH Keywords: complete convergence
zbMATH Keywords: probabilistic normed space
zbMATH Keywords: probabilistic form
MaRDI profile type: Publication
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full work available at URL: s0022-247x(02)00577-2
OpenAlex ID: W2000675160
description: scientific article; zbMATH DE number 1915601