When van Lambalgen’s Theorem fails

DOI10.1090/S0002-9939-06-08541-8zbMath1110.03027MaRDI QIDQ3420060

Liang Yu

Publication date: 1 February 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Cantor spaceSchnorr randomnesscomputable randomness.

Mathematics Subject Classification ID

Algorithmic information theory (Kolmogorov complexity, etc.) (68Q30) Other Turing degree structures (03D28)

Related Items (11)

Reducibilities relating to Schnorr randomness ⋮ Schnorr randomness for noncomputable measures ⋮ Russell's typicality as another randomness notion ⋮ Finite-state relative dimension, dimensions of AP subsequences and a finite-state van Lambalgen's theorem ⋮ Computability theory. Abstracts from the workshop held April 25 -- May 1, 2021 (hybrid meeting) ⋮ On Resource-Bounded Versions of the van Lambalgen Theorem ⋮ Truth-table Schnorr randomness and truth-table reducible randomness ⋮ Jump inversions inside effectively closed sets and applications to randomness ⋮ Effective dimension of points visited by Brownian motion ⋮ Uniform van Lambalgen's theorem fails for computable randomness ⋮ Unified characterizations of lowness properties via Kolmogorov complexity

Cites Work

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• Algorithmic Randomness and Complexity
• Von Mises' definition of random sequences reconsidered
• Schnorr randomness
• Classes of Recursively Enumerable Sets and Degrees of Unsolvability
• A unified approach to the definition of random sequences
• The definition of random sequences
• Randomness, relativization and Turing degrees

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