On extreme points of Orlicz spaces with Orlicz norm

In the paper we consider a class of Orlicz spaces equipped with the Orlicz norm over a non-negative, complete and $\sigma$-finite measure space $(T,\Sigma,\mu)$, which covers, among others, Orlicz spaces isomorphic to $L^\infty$ and the interpolation space $L^1+L^\infty$. We give some necessary conditions for a point $x$ from the unit sphere to be extreme. Applying this characterization, in the case of an atomless measure $\mu$, we find a description of the set of extreme points of $L^1+L^\infty$ which corresponds with the result obtained by R.Grza\'{s}lewicz and H.Schaefer [3] and H.Schaefer [13].