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Eighth International Conference on Computability, Complexity and Randomness (CCR 2013)

September 23–27, 2013, Moscow, Russia

Continuous higher randomness

Benoit Monin
We survey recent results in the theory of higher randomness. We emphasize the role of continuous functions in the theory of randomness. This leads to finding the correct generalisation of Turing reducibility in the higher context, and thus to continuous relativisations of higher ML-randomness. However, some oracles misbehave, leading to the separation of notions which coincide in countable randomness.