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On the Deterministic and Asymptotic σ-Algebras of a Markov Operator
Published online by Cambridge University Press: 20 November 2018
Abstract
Let P be a Markov operator on L∞(X, Σ, m) which does not disappear (i.e., P1A ≡ 0 => 1A ≡ 0 ) . We study the relationship between 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.
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- Copyright © Canadian Mathematical Society 1989
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