A constructive view on ergodic theorems
Bas Spitters
Source: J. Symbolic Logic Volume 71, Issue 2
(2006), 611-623.
Abstract
Let T be a positive L₁-L∞ contraction. We prove that the following statements are equivalent in constructive mathematics.
- 1. The projection in L₂ on the space of invariant functions exists;
- 2. The sequence (Tⁿ)n ∈ N Cesáro-converges in the L₂ norm;
- 3. The sequence (Tⁿ)n ∈ N Cesáro-converges almost everywhere.
As a corollary we obtain a constructive ergodic theorem for ergodic measure-preserving transformations. This answers a question posed by Bishop.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1146620162
Digital Object Identifier: doi:10.2178/jsl/1146620162
Mathematical Reviews number (MathSciNet): MR2225897
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