The algebraic structure of spaces of integrable functions - Marco Abbadini

We characterize the functions from R^I to R that preserve integrability, meaning that their pointwise application maps any I-tuple of integrable functions to an integrable function (as, for example, the addition). We show that Dedekind sigma-complete truncated vector lattices are precisely the algebras with integrability-preserving functions as function symbols and that satisfy all equations true in R. We also show that an analogous study restricted to finite measure spaces gives the class of Dedekind sigma-complete vector lattices with weak unit. Furthermore, we provide concrete models for free algebras in these categories.