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Corpus ID: 54459720

On the close interaction between algorithmic randomness and constructive/computable measure theory

@article{Rute2018OnTC,
title={On the close interaction between algorithmic randomness and constructive/computable measure theory},
author={Jason Rute},
journal={ArXiv},
year={2018},
volume={abs/1812.03375}
}

This is a survey of constructive and computable measure theory with an emphasis on the close connections with algorithmic randomness. We give a brief history of constructive measure theory from Brouwer to the present, emphasizing how Schnorr randomness is the randomness notion implicit in the work of Brouwer, Bishop, Demuth, and others. We survey a number of recent results showing that classical almost everywhere convergence theorems can be used to characterize many of the common randomness… Expand