It is shown that the only Luxemburg functionals that satisfy a very simply formulated property are induced by \(p\)th-power functions, \(0\lt p\lt \infty\). The known result that Orlicz spaces cannot be normed analogously to \(L_p\)-spaces follows as a consequence.
"A characterization of Orlicz functions producing an additive property." Real Anal. Exchange 21 (2) 629 - 636, 1995/1996.