Suppose that μ is a nonnegative finite regular Borel measure on an infinite compact abelian group Γ. Let M be a finite subset of the dual group G of Γ. It is shown that if p ∈ (0, 1), then the linear span of GobM is dense in Lp(μ). The result is extended to Lp-spaces of operator-valued functions which are p-integrable with respect to certain operator-valued measures. An application to a theorem by Koosis is given.