Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T07:28:16.335Z Has data issue: false hasContentIssue false
  • English
  • Français

SETS OF UNIQUENESS OF SERIES OF STOCHASTICALLY INDEPENDENT FUNCTIONS

Published online by Cambridge University Press:  14 October 2002

Francisco J. Freniche  and
Ricardo Ríos-Collantes-de-Terán
Francisco J. Freniche
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Sevilla 41080, Spain ([email protected]; [email protected])
Ricardo Ríos-Collantes-de-Terán
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Sevilla 41080, Spain ([email protected]; [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that, for every sequence $(f_n)$ of stochastically independent functions defined on $[0,1]$—of mean zero and variance one, uniformly bounded by $M$—if the series $\sum_{n=1}^\infty a_nf_n$ converges to some constant on a set of positive measure, then there are only finitely many non-null coefficients $a_n$, extending similar results by Stechkin and Ul’yanov on the Rademacher system. The best constant $C_M$ is computed such that for every such sequence $(f_n)$ any set of measure strictly less than $C_M$ is a set of uniqueness for $(f_n)$.

AMS 2000 Mathematics subject classification:Primary 42C25. Secondary 60G50

Keywords

set of uniquenessstochastically independent systemset of constancy
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 3 , October 2002 , pp. 557 - 563
Copyright
Copyright © Edinburgh Mathematical Society 2002