Superporosity in a class of non-normable spaces

Abstract

Let \(\mathcal M\) stand for the space of all \(S\)-measurable real functions on the infinite \(\sigma\)-finite measure space \((X,S,\mu)\) endowed with the (metrizable but non-normable) topology of convergence in measure on sets of finite measure. Some natural subsets (including the \(L_p\)-spaces) are proved to be sigma-superporous in \(\mathcal M\). The possibility of finding non-sigma-porous meager sets in this non-normable setting is discussed.