Abstract
A theorem of Ku\(\mathrm{\check{c}}\)era 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.
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Bienvenu, L., Day, A., Mezhirov, I., Shen, A. (2010). Ergodic-Type Characterizations of Algorithmic Randomness. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_6
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DOI: https://doi.org/10.1007/978-3-642-13962-8_6
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