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March 2007 The pointwise ergodic theorem in subsystems of second-order arithmetic
Ksenija Simic
J. Symbolic Logic 72(1): 45-66 (March 2007). DOI: 10.2178/jsl/1174668383

Abstract

The pointwise ergodic theorem is nonconstructive. In this paper, we examine origins of this non-constructivity, and determine the logical strength of the theorem and of the auxiliary statements used to prove it. We discuss properties of integrable functions and of measure preserving transformations and give three proofs of the theorem, though mostly focusing on the one derived from the mean ergodic theorem. All the proofs can be carried out in ACA₀; moreover, the pointwise ergodic theorem is equivalent to (ACA) over the base theory RCA₀.

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Ksenija Simic. "The pointwise ergodic theorem in subsystems of second-order arithmetic." J. Symbolic Logic 72 (1) 45 - 66, March 2007. https://doi.org/10.2178/jsl/1174668383

Information

Published: March 2007
First available in Project Euclid: 23 March 2007

zbMATH: 1116.03056
MathSciNet: MR2298470
Digital Object Identifier: 10.2178/jsl/1174668383

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 1 • March 2007
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