Ergodic theorems for individual random sequences
Theoretical Computer Science - Special issue Kolmogorov complexity
Computable analysis: an introduction
Computable analysis: an introduction
Random elements in effective topological spaces with measure
Information and Computation
Uniform test of algorithmic randomness over a general space
Theoretical Computer Science
An effective ergodic theorem and some applications
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Computability of probability measures and Martin-Löf randomness over metric spaces
Information and Computation
Applications of Effective Probability Theory to Martin-Löf Randomness
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Computable Exchangeable Sequences Have Computable de Finetti Measures
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Ergodic-type characterizations of algorithmic randomness
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
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The interaction between algorithmic randomness and ergodic theory is a rich field of investigation. In this paper we study the particular case of the ergodic decomposition. We give several positive partial answers, leaving the general problem open. We shortly illustrate how the effectivity of the ergodic decomposition allows one to easily extend results from the ergodic case to the non-ergodic one (namely Poincaré recurrence theorem). We also show that in some cases the ergodic measures can be computed from the typical realizations of the process.