Finitely additive representation of Lp spaces

Let be any atomless and countably additive probability measure on the product space N{0,1} with the usual σ-algebra. Then there is a purely finitely additive probability measure λ on the power set of a countable subset such that can be isometrically isomorphically embedded as a closed subspace of Lp(λ). The embedding is strict. It is also ‘canonical,’ in the sense that it maps simple and continuous functions on to their restrictions to T.