Bishop's (up)crossing inequality and lower semicomputable random reals revisited

November 12, 2025 · The Ethereal · 🏛 arXiv.org

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Authors Mikhail Andreev, Alexander Shen arXiv ID 2511.09756 Category math.LO: Logic Cross-listed cs.IT Citations 0 Venue arXiv.org Last Checked 1 month ago
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.
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