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 L p which are in no other L q 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.