Geodesic
On Products of Conditional Expectation Operators
Canadian mathematical bulletin, Tome 33 (1990) no. 3, pp. 257-260

Voir la notice de l'article provenant de la source Cambridge University Press

Let (X, Σ, μ) be a probability space, let f1 , f2 , ..., Fk be k σ-subalgebras of Σ, and let p ∊ R be such that 1 < p < + ∞. Let Pi :LP(X, Σ, μ) → LP(X, Σ, μ) be the conditional expectation operator corresponding to fi for every i = 1,2,..., k, and set T = P1 . . . Pk. Our goal in the note is to give a new and simpler proof of the fact that for every f ∊ LP(X, Σ, μ), the sequence (Tnf)n∊N converges in the norm topology of LP(X, Σ, μ), and that its limit is the conditional expectation of f with respect to f1 ∩ f2 ∩ ... ∩ Fk.
DOI : 10.4153/CMB-1990-041-3
Mots-clés : 47A35, 28D99 
Zaharopol, Radu. On Products of Conditional Expectation Operators. Canadian mathematical bulletin, Tome 33 (1990) no. 3, pp. 257-260. doi: 10.4153/CMB-1990-041-3
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