Porosity of \(X^\Phi \) Spaces

Abstract

This paper aims to extend several well-known theorems regarding porosity in Lebesgue and Orlicz spaces to generalized Orlicz spaces associated with quasi-Banach spaces. We will explore the implications of these extensions and provide a comprehensive analysis of their significance in the broader context of functional analysis. Additionally, we will present results concerning homogeneous spaces, and relationships with the generalized Orlicz spaces.