# Algorithmic randomness and stochastic selection function

@article{Takahashi2012AlgorithmicRA, title={Algorithmic randomness and stochastic selection function}, author={Hayato Takahashi}, journal={ArXiv}, year={2012}, volume={abs/1205.5504} }

We show algorithmic randomness versions of the two classical theorems on subsequences of normal numbers. One is Kamae-Weiss theorem (Kamae 1973) on normal numbers, which characterize the selection function that preserves normal numbers. Another one is the Steinhaus (1922) theorem on normal numbers, which characterize the normality from their subsequences. In van Lambalgen (1987), an algorithmic analogy to Kamae-Weiss theorem is conjectured in terms of algorithmic randomness and complexity. In…

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