Bishop's (up)crossing inequality and lower semicomputable random reals revisited
Logic
2026-05-05 v2 Information Theory
math.IT
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.
Keywords
Cite
@article{arxiv.2511.09756,
title = {Bishop's (up)crossing inequality and lower semicomputable random reals revisited},
author = {Mikhail Andreev and Alexander Shen},
journal= {arXiv preprint arXiv:2511.09756},
year = {2026}
}
Comments
Accepted by Computability in Europe conference 2026