Bishop's (up)crossing inequality and lower semicomputable random reals revisited
arXiv:2511.09756
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 factor) by noting that it immediately follows from Bishop's upcrossing inequality. We also provide a simple derivation of this inequality.
Accepted by Computability in Europe conference 2026