On \((C,\alpha)\)-summability almost everywhere of certain sequences
type: Item
instance of: scholarly article
title: On \((C,\alpha)\)-summability almost everywhere of certain sequences
zbMATH Open document ID: 0809.60035
DOI: 10.1007/BF01212592
author: V. F. Gaposhkin
published in: Mathematical Notes
publication date: 1994-07-13T00:00:00Z
review text: In the first part of this paper the author gives a new proof of a result concerning the \((C,\alpha)\)-summability of a sequence of identically distributed independent random numbers and its generalization to sequences of martingale differences. In the second part he considers conditions of \((C, \alpha)\)-summability a.e. of a sequence of powers of the operator \((T^ nf)\), and proves the equivalence of the Cesàro \((C,\alpha)\)-method for all \(\alpha > 1/2\) and the Abel method in the problem of convergence a.e. for any normal contraction in \(L_ 2\).
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 589629
zbMATH Keywords: summability
zbMATH Keywords: ergodic theorem
zbMATH Keywords: strong law of large numbers
reviewed by: Wen Liu
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01212592
OpenAlex ID: W2047164653
description: scientific article; zbMATH DE number 589629