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Uncomputably Noisy Ergodic Limits

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journal contribution
posted on 01.10.2011 by Jeremy Avigad

V’yugin has shown that there are a computable shift-invariant measure on 2N and a simple function f such that there is no computable bound on the rate of convergence of the ergodic averages Anf. 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 ε.

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© 2012 by University of Notre Dame

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01/10/2011

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