Lattice-embeddingL p into Orlicz spaces

Given 0<α≤p≤β<∞, we construct Orlicz function spacesL ^F 0, 1] with Boyd indicesα andβ such thatL ^p is lattice isomorphic to a sublattice ofL ^F 0, 1]. Forp>2 this shows the existence of (non-trivial) separable r.i. spaces on 0, 1] containing an isomorphic copy ofL ^p . The discrete case of Orlicz spaces ℓ ^F (I) containing an isomorphic copy of ℓ ^p (Γ) for uncountable sets Γ ⊂I is also considered. Supported in part by DGICYT, grant PB91-0377.