Probability (2nd ed.)
Ergodic theorems for individual random sequences
Theoretical Computer Science - Special issue Kolmogorov complexity
Computability of probability measures and Martin-Löf randomness over metric spaces
Information and Computation
Randomness and the ergodic decomposition
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
A constructive version of Birkhoff's ergodic theorem for Martin-Löf random points
Information and Computation
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A theorem of Kučera states that given a Martin-Löf random infinite binary sequence ω and an effectively open set A of measure less than 1, some tail of ω is not in A. We show that this result can be seen as an effective version of Birkhoff's ergodic theorem (in a special case). We prove several results in the same spirit and generalize them via an effective ergodic theorem for bijective ergodic maps.