Date of Original Version

10-2011

Type

Article

Rights Management

© 2012 by University of Notre Dame

Abstract or Description

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.

DOI

10.1215/00294527-1716757

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Published In

Notre Dame Journal of Formal Logic, 53, 3, 347-350.