Geodesic
On the Deterministic and Asymptotic σ-Algebras of a Markov Operator
Canadian mathematical bulletin, Tome 32 (1989) no. 1, pp. 64-73

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Let P be a Markov operator on L ∞(X, Σ, m) which doesnot disappear (i.e., P1A ≡ 0 => 1A ≡ 0 ) . We study the relationshipbetween the σ-algebras (the deterministicσ-algebra), and the asymptoticσ-algebra When m is a σ-finite invariant measure, measurable iff p*npnf = f, and also iff Pnf has the same distribution as f . The case of a convolution operator on a locally compact group is considered.
DOI : 10.4153/CMB-1989-009-2
Mots-clés : 60J05, 60J15:, 47A35 
Krengel, Ulrich; Lin, Michael. On the Deterministic and Asymptotic σ-Algebras of a Markov Operator. Canadian mathematical bulletin, Tome 32 (1989) no. 1, pp. 64-73. doi: 10.4153/CMB-1989-009-2
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     author = {Krengel, Ulrich and Lin, Michael},
     title = {On the {Deterministic} and {Asymptotic} {\ensuremath{\sigma}-Algebras} of a {Markov} {Operator}},
     journal = {Canadian mathematical bulletin},
     pages = {64--73},
     year = {1989},
     volume = {32},
     number = {1},
     doi = {10.4153/CMB-1989-009-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-009-2/}
}
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