Strictly singular inclusions into \(L^1 + L^\infty\)

It is given a complete characterization of the strict singularity and the disjoint strict singularity of the inclusions E ↪ L1 + L∞ for the class of rearrangement invariant function spaces E on the \([0,\infty)\) interval. Their relationship is also analyzed. Suitable criteria are given involving the scale of order continuous weak Lp-spaces for \(1 < p < \infty\) .