Finitely additive representation of Lp spaces

Nabil I. Al-Najjar*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let over(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 ⊂ over(T, ̄) such that Lp (over(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 over(T, ̄) to their restrictions to T.

Original languageEnglish (US)
Pages (from-to)891-899
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume330
Issue number2
DOIs
StatePublished - Jun 15 2007

Keywords

  • Finitely additive probabilities
  • L spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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