Next Article in Journal
Dispersive Soliton Solutions and Dynamical Analyses of a Nonlinear Model in Plasma Physics
Previous Article in Journal
Optimal Hölder Regularity for Discontinuous Sub-Elliptic Systems Structured on Hörmander’s Vector Fields
Previous Article in Special Issue
On the Strong Convergence of Combined Generalized Equilibrium and Fixed Point Problems in a Banach Space
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Axioms
Volume 14
Issue 10
10.3390/axioms14100762
axioms-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

The Brooks–Chacon Biting Lemma, the Castaing–Saadoune Procedure, and the Baum–Katz Theorem Along Subsequences

by
George Stoica
1,*,
Deli Li
2 and
Liping Liu
2
1
Department of Mathematics and Statistics, University of New Brunswick, Saint John, NB E2K 5E2, Canada
2
Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON P7B 5E1, Canada
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(10), 762; https://doi.org/10.3390/axioms14100762 (registering DOI)
Submission received: 9 September 2025 / Revised: 10 October 2025 / Accepted: 12 October 2025 / Published: 14 October 2025
(This article belongs to the Special Issue Research on Functional Analysis and Its Applications)
Versions Notes

Abstract

We show how the Brooks–Chacon Biting Lemma can be combined with the Castaing–Saadoune procedure to provide the complete rate of convergence along subsequences when the uniformly boundedness condition is violated.
Keywords: complete convergence; boundedness hypotheses; law of large numbers complete convergence; boundedness hypotheses; law of large numbers

Share and Cite

MDPI and ACS Style

Stoica, G.; Li, D.; Liu, L. The Brooks–Chacon Biting Lemma, the Castaing–Saadoune Procedure, and the Baum–Katz Theorem Along Subsequences. Axioms 2025, 14, 762. https://doi.org/10.3390/axioms14100762

AMA Style

Stoica G, Li D, Liu L. The Brooks–Chacon Biting Lemma, the Castaing–Saadoune Procedure, and the Baum–Katz Theorem Along Subsequences. Axioms. 2025; 14(10):762. https://doi.org/10.3390/axioms14100762

Chicago/Turabian Style

Stoica, George, Deli Li, and Liping Liu. 2025. "The Brooks–Chacon Biting Lemma, the Castaing–Saadoune Procedure, and the Baum–Katz Theorem Along Subsequences" Axioms 14, no. 10: 762. https://doi.org/10.3390/axioms14100762

APA Style

Stoica, G., Li, D., & Liu, L. (2025). The Brooks–Chacon Biting Lemma, the Castaing–Saadoune Procedure, and the Baum–Katz Theorem Along Subsequences. Axioms, 14(10), 762. https://doi.org/10.3390/axioms14100762

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Article metric data becomes available approximately 24 hours after publication online.
Back to TopTop