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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:
 [1] Foundations of constructive analysis (1967) · Zbl 0183.01503 [2] Constructive analysis 279 (1985) · Zbl 0656.03042 [3] Intuitionism and Proof Theory (Proceedings of the summer conference at Buffalo, N.Y., 1968) pp 53– (1970) [4] Annals of Pure and Applied Logic [5] An introduction to ergodic theory 79 (1982) [6] Linear operators. Part I: General theory (1958) [7] Ergodic theory (1983) [8] DOI: 10.1090/S0002-9947-1972-0291411-3 [9] Ergodic theorems (1985) [10] DOI: 10.1090/S0002-9939-03-07067-9 · Zbl 1128.46030 [11] Transactions of the American Mathematical Society 216 pp 393– (1976)
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