A constructive version of Birkhoff's ergodic theorem for Martin-Löf random points
The authors prove a constructive version of Birkhoff's ergodic theorem for Martin-Löf random reals and effectively open sets. From the proof one can extract a new simple proof of the effective ergodic theorem. The main result was independently obtained by \textit{J. N. Y Franklin}, \textit{N. Greenberg}, \textit{J. S. Miller} and \textit{K. M. Ng} in [``Martin-Löf random points satisfy Birkhoff's ergodic theorem for effectively closed sets'', Proc. Am. Math. Soc. 140, No. 10, 3623--3628 (2012; \url{doi:10.1090/S0002-9939-2012-11179-7})].
scientific article; zbMATH DE number 6038284
scientific article