Lindeberg-Feller theorems on Lie groups
type: Item
instance of: scholarly article
title: Lindeberg-Feller theorems on Lie groups
zbMATH Open document ID: 0941.60018
published in: Archiv der Mathematik
publication date: 1999-06-28T00:00:00Z
full work available at URL: http://hdl.handle.net/2437/166270
review text: Let \(G\) be a Lie group. A convolution semigroup \((\mu_t)_{t\geq 0}\) of nondegenerate measures is called a Gaussian semigroup if \(\lim_{t\to 0}t^{-1}\mu_t(G\setminus U)= 0\) for each neighborhood \(U\) of \(e\). A probability measure \(\mu\) on \(G\) is called a Gaussian measure if there exists a Gaussian semigroup \((\mu_t)_{t\geq 0}\) such that \(\mu_1= \mu\). The author obtains necessary and sufficient conditions for the triangular array \((\mu_{nl})_{l= 1,\dots, k_n;n\geq 1}\) of probability measures on \(G\) to converge to a Gaussian measure.
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1309370
zbMATH Keywords: Lie group
zbMATH Keywords: Gaussian measure
author: Gyula Pap
MaRDI profile type: Publication
OpenAlex ID: W1983499176
Wikidata QID: Q115390133
DOI: 10.1007/S000130050340
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description: scientific article; zbMATH DE number 1309370