Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 53, Number 3 (2012), 347-350.
Uncomputably Noisy Ergodic Limits
V’yugin has shown that there are a computable shift-invariant measure on and a simple function such that there is no computable bound on the rate of convergence of the ergodic averages . Here it is shown that in fact one can construct an example with the property that there is no computable bound on the complexity of the limit; that is, there is no computable bound on how complex a simple function needs to be to approximate the limit to within a given .
Notre Dame J. Formal Logic Volume 53, Number 3 (2012), 347-350.
First available in Project Euclid: 25 September 2012
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Avigad, Jeremy. Uncomputably Noisy Ergodic Limits. Notre Dame J. Formal Logic 53 (2012), no. 3, 347--350. doi:10.1215/00294527-1716757. https://projecteuclid.org/euclid.ndjfl/1348577704