**Stephen Montgomery-Smith and Evgueni Semenov, Embeddings of rearrangement invariant spaces that are not strictly singular.**
*Positivity, ***4**, (2000), 397-404.
We give partial answers to the following conjecture: the natural embedding of a rearrangement invariant space \(E\) into \(L_1([0,1])\) is strictly singular if and only if \(G\) does not embed into \(E\) continuously, where \(G\) is the closure of the simple functions in the Orlicz space \(L_\Phi\) with \(\Phi(x) = \exp(x^2)-1\).
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