Topological and topological linear properties of the Sugeno-Lorentz spaces

TL;DR

This paper investigates fundamental topological and linear properties of Sugeno-Lorentz spaces, extending previous research on their completeness and separability, and highlighting differences from classical Lebesgue spaces.

Contribution

It provides a detailed analysis of the topological and linear properties of Sugeno-Lorentz spaces, advancing understanding beyond prior work on their completeness and separability.

Findings

Sugeno-Lorentz spaces exhibit unique topological properties.

The paper establishes new results on the linear structure of these spaces.

Differences from classical Lebesgue spaces are highlighted.

Abstract

The properties of the spaces of Sugeno integrable functions are quite different from those of the ordinary spaces of Lebesgue integrable functions. The purpose of the paper is to further advance our study of the Sugeno-Lorentz spaces, in which the completeness and separability of the spaces were discussed. As a continuation of our previous research, in this paper, some fundamental topological and topological linear properties of the Sugeno-Lorentz spaces are investigated in detail.