Iterates of a product of conditional expectation operators

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9 Scopus citations


Let (Ω, F, μ) be a probability space and let T = P1 P2 ⋯ Pd be a finite product of conditional expectations with respect to the sub σ-algebras F1, F2, ..., Fd. We show that for every f ∈ Lp (μ), 1 < p ≤ 2, the sequence {Tn f} converges μ-a.e., withunder(lim, n → ∞) Tn f = E [f | F1 ∩ F2 ∩ ⋯ ∩ Fd] μ -a.e.

Original languageEnglish
Pages (from-to)658-668
Number of pages11
JournalJournal of Functional Analysis
Issue number2
StatePublished - 15 Jan 2007
Externally publishedYes


  • Almost everywhere convergence
  • Cesàro summability
  • Complex interpolation
  • Conditional expectations
  • Maximal inequality
  • Spectral sets

ASJC Scopus subject areas

  • Analysis


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