Finitely additive representation of L spaces
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چکیده
Let λ̄ 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 ⊂ T̄ such that Lp(λ̄) 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 T̄ to their restrictions to T . © 2006 Elsevier Inc. All rights reserved.
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تاریخ انتشار 2007