Superporosity in a class of non-normable spaces (Q5918085)

Let \((\mathcal M,\rho)\) be the space of all \(S\)-measurable real functions on the infinite \(\sigma \)-finite measure space \((X,S,\mu)\) with the metric \(\rho \), which gives the topology of convergence in measure on sets of finite measure. The author shows that certain subsets (e.g., \(L^p\)) of \(\mathcal M\) form \(\sigma \)-superporous subsets of \(\mathcal M\) (see \textit{L. Zajíček} [Real Anal. Exch. 13, No.~2, 314-350 (1988; Zbl 0666.26003)], for definition and details). Let us note that the first question posed by the author in Remark 3 (concerning a Fubini-type theorem for porous sets) was negatively answered in [\textit{D. Preiss} and \textit{L. Zajíček}, Real Anal. Exch. 24, No. 1, 295-313 (1998)].