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

Mikhail Andreev; Alexander Shen

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arXiv · 2511.09756

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

Mikhail Andreev·Alexander Shen

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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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BibTeX RIS

Mikhail Andreev, Alexander Shen. 2025-11-12. Bishop's (up)crossing inequality and lower semicomputable random reals revisited. https://arxiv.org/abs/2511.09756

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