Bishop's (up)crossing inequality and lower semicomputable random reals revisited
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.