Law of large numbers in a Banach space
type: Item
instance of: scholarly article
title: Law of large numbers in a Banach space
zbMATH Open document ID: 0536.60012
DOI: 10.1007/BF00966470
published in: Lithuanian Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: It is well known that the law of large numbers (LLN) holds in its classical form for random variables taking values in a Banach space of type r, \(1\leq r<2\). The author presents sufficient conditions for the LLN to hold in a certain relatively wide class of Banach spaces. This class contains spaces of cotype r, \(1\leq r<2\), in the sense of \textit{D. Kh. Mushtari} [Teor. Veroyatn. Primen. 25, 105-118 (1980; Zbl 0441.60007); English translation in Theory Probab. Appl. 25, 105-117 (1980)] and is defined via some properties of stable distributions.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 46B99
zbMATH DE Number: 3852098
zbMATH Keywords: law of large numbers
zbMATH Keywords: stable distribution
Wikidata QID: Q114852797
author: Alfredas Račkauskas
MaRDI profile type: Publication
cites work: Inequalities for B-valued random vectors with applications to the strong law of large numbers
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description: scientific article; zbMATH DE number 3852098