Abstract Let E be a Banach space, let (Ω, Σ, μ) a finite measure space, let 1 < p < ∞ and let L p (μ; E ) the Banach space of all E -valued p -Bochner μ -integrable functions with its usual norm. In this note it is shown that E contains a complemented subspace isomorphic to l 1 if (and only if) L p (μ; E ) does. An extension of this result is also given.