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Bishop's (up)crossing inequality and lower semicomputable random reals revisited
Mikhail Andreev, Alexander Shen · 2025-11-13 · via cs.IT updates on arXiv.org

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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