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

DOI

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
@article{10_4153_CMB_1990_041_3,
     author = {Zaharopol, Radu},
     title = {On {Products} of {Conditional} {Expectation} {Operators}},
     journal = {Canadian mathematical bulletin},
     pages = {257--260},
     year = {1990},
     volume = {33},
     number = {3},
     doi = {10.4153/CMB-1990-041-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-041-3/}
}
TY  - JOUR
AU  - Zaharopol, Radu
TI  - On Products of Conditional Expectation Operators
JO  - Canadian mathematical bulletin
PY  - 1990
SP  - 257
EP  - 260
VL  - 33
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-041-3/
DO  - 10.4153/CMB-1990-041-3
ID  - 10_4153_CMB_1990_041_3
ER  - 
%0 Journal Article
%A Zaharopol, Radu
%T On Products of Conditional Expectation Operators
%J Canadian mathematical bulletin
%D 1990
%P 257-260
%V 33
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-041-3/
%R 10.4153/CMB-1990-041-3
%F 10_4153_CMB_1990_041_3

Cité par Sources :