Journal of Symbolic Logic 72 (1):45 - 66 (2007)

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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1174668383
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 60,920
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

The Metamathematics of Ergodic Theory.Jeremy Avigad - 2009 - Annals of Pure and Applied Logic 157 (2-3):64-76.

Add more citations

Similar books and articles

Fundamental Notions of Analysis in Subsystems of Second-Order Arithmetic.Jeremy Avigad - 2006 - Annals of Pure and Applied Logic 139 (1):138-184.
A Constructive View on Ergodic Theorems.Bas Spitters - 2006 - Journal of Symbolic Logic 71 (2):611 - 623.
A Note on Goodman's Theorem.Ulrich Kohlenbach - 1999 - Studia Logica 63 (1):1-5.
Formalizing Forcing Arguments in Subsystems of Second-Order Arithmetic.Jeremy Avigad - 1996 - Annals of Pure and Applied Logic 82 (2):165-191.
Ergodic Theorems and the Basis of Science.Karl Petersen - 1996 - Synthese 108 (2):171 - 183.
Predicative Fragments of Frege Arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.
Quantum Mathematics.J. Michael Dunn - 1980 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
Stephen G. Simpson Subsystems of Second-Order Arithmetic.Jeffrey Ketland - 2001 - British Journal for the Philosophy of Science 52 (1):191-195.


Added to PP index

Total views
5 ( #1,156,179 of 2,439,320 )

Recent downloads (6 months)
1 ( #434,168 of 2,439,320 )

How can I increase my downloads?


My notes