Bishop's (up)crossing inequality and lower semicomputable random reals revisited
Authors
Mikhail Andreev
Alexander Shen
Abstract
In this paper we provide an easy proof of Barmpalias--Lewis-Pye result saying that all computable increasing sequences converging to random reals converge with the same speed (up to a $c+o(1)$ factor) by noting that it immediately follows from Bishop's upcrossing inequality. We also provide a simple derivation of this inequality.
