On relation between statistical ideal and ideal generated by a modulus function

TL;DR

This paper characterizes specific modulus functions whose generated ideals coincide with the statistical ideal, clarifying the relationship between these mathematical constructs.

Contribution

It provides a characterization of modulus functions that generate ideals equal to the statistical ideal, advancing understanding in this area of mathematical analysis.

Findings

Identifies conditions under which the ideal generated by a modulus function equals the statistical ideal.

Provides a complete characterization of such modulus functions.

Enhances the theoretical framework connecting modulus functions and statistical ideals.

Abstract

We characterize those modulus functions $f$ for which the ideal generated by $f$ is equal to the statistical ideal.