In this chapter, we discuss computable presentations of another kind of Banach space, the Lebesgue spaces. Recall that a Banach space is an \(L^p\) space space if it is isomorphic to \(L^p(\Omega )\) for some measure space \(\Omega \) and that a Banach space is a LebesgueLebesgue space space if it is an \(L^p\) space for some \(p \in [1, \infty ]\) . Our field of scalars \(\mathbb {F}\) can be either \(\mathbb {R}\) or \(\mathbb {C}\) . As is customary in measure theory, we identify sets that differ only on a set of measure zero, and we identify functions that differ only on a set of measure zero.