Finitely additive representation of Lp spaces

Let ¯λ be any atomless and countably additive probability measure on the product space {0, 1}N with the usual σ-algebra. Then there is a purely finitely additive probability measure λ on the power set of a countable subset T ⊂ T¯ such that Lp(λ¯) 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 T¯ to their restrictions to T . © 2006 Elsevier Inc. All rights reserved