Some limit theorems of almost periodic function systems under the relative measure
type: Item
instance of: scholarly article
title: Some limit theorems of almost periodic function systems under the relative measure
zbMATH Open document ID: 0668.60030
author: Katusi Fukuyama
published in: Journal of Mathematics of Kyoto University
publication date: 1988-01-01T00:00:00Z
review text: \textit{M. Kac} and \textit{H. Steinhaus} [Stud. Math. 7, 1-15 (1938; Zbl 0018.07601)] proved that if a real sequence \(\{\lambda_ j\}\) is algebraically independent, then the sequence \(\{\) \(\sqrt{2} \cos \lambda_ jx\}\) obeys the CLT. The first aim of the present author is to weaken the condition on \(\{\lambda_ j\}\) by introducing the notion of signed sum condition. Second, he proves a SLLN. Third, he proves a functional CLT of Prohorov type and derives other limit theorems. Finally, he proves a functional (i.e. Strassen type) LIL. These results are treated in the framework of uniformly bounded (strongly or equinormed) multiplicative systems defined by \textit{G. Alexits} [Convergence problems of orthogonal series (1961; Zbl 0098.274)].
reviewed by: Ferenc Móricz
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 4094493
zbMATH Keywords: functional central limit theorem
zbMATH Keywords: multiplicative systems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520403
OpenAlex ID: W1575449177
DOI: 10.1215/KJM/1250520403
description: scientific article; zbMATH DE number 4094493