Spaceability of strict order integrability

In this paper, sharp conditions on a measure space are provided in order that the subset of functions in the corresponding Lebesgue space Lp which are in no other Lq contains, except for zero, an infinite dimensional closed subspace. This completes earlier work of several authors. The main result is derived from a new, general criterion for spaceability on function spaces. A further application to spaceability of the class of non-absolutely continuous functions is supplied.