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A constructive view on ergodic theorems. (English) Zbl 1106.03052
J. Symb. Log. 71, No. 2, 611-623 (2006); corrigendum ibid. 71, No. 4, 1431-1432 (2006).
Through equivalence proofs (in constructive mathematics) of a set of three statements (involving projections in \(L_2\) and Cesaro-convergence), necessary and sufficient conditions for the Mean Ergodic Theorem and the Dunford-Schwartz Pointwise Ergodic Theorem are found. A constructive ergodic theorem for ergodic measure-preserving transformations is proven, so providing an answer to a question posed by E. Bishop.

MSC:
03F60 Constructive and recursive analysis
37A05 Dynamical aspects of measure-preserving transformations
28D05 Measure-preserving transformations
46S30 Constructive functional analysis
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References:
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