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A subspace $H$ of a rearrangement invariant space $X$ on $[0,1]$ is stronglyembedded in $X$ if, in $H$, convergence in $X$-norm is equivalent toconvergence in measure. We obtain necessary and sufficient conditions on anOrlicz function $M$, under which the unit ball of an arbitrary stronglyembedded subspace in the Orlicz space $L_M$ has equi-absolutely continuousnorms in $L_M$.

The structure of subspaces in Orlicz spaces between $L^1$ and $L^2$