Journal of Symbolic Logic

The pointwise ergodic theorem in subsystems of second-order arithmetic

Ksenija Simic

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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.

Article information

Source
J. Symbolic Logic, Volume 72, Issue 1 (2007), 45-66.

Dates
First available in Project Euclid: 23 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1174668383

Digital Object Identifier
doi:10.2178/jsl/1174668383

Mathematical Reviews number (MathSciNet)
MR2298470

Zentralblatt MATH identifier
1116.03056

Citation

Simic, Ksenija. The pointwise ergodic theorem in subsystems of second-order arithmetic. J. Symbolic Logic 72 (2007), no. 1, 45--66. doi:10.2178/jsl/1174668383. https://projecteuclid.org/euclid.jsl/1174668383


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