Randomness for non-computable measures

DOI10.1090/S0002-9947-2013-05682-6zbMath1307.03026MaRDI QIDQ2846975

Joseph S. Miller, Adam R. Day

Publication date: 4 September 2013

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

zbMATH Keywords

randomnessneutral measurenoncomputable measurePA-complete Turing degree

Mathematics Subject Classification ID

Algorithmic information theory (Kolmogorov complexity, etc.) (68Q30) Other degrees and reducibilities in computability and recursion theory (03D30) Algorithmic randomness and dimension (03D32)

Related Items

Energy randomness, UNIVERSAL CODING AND PREDICTION ON ERGODIC RANDOM POINTS, A STRUCTURAL DICHOTOMY IN THE ENUMERATION DEGREES, Continuous randomness via transformations of 2-random sequences, Schnorr randomness for noncomputable measures, Martin-Löf random generalized Poisson processes, COMPUTABLY COMPACT METRIC SPACES, Turing degrees and randomness for continuous measures, Independence, relative randomness, and PA degrees, How much randomness is needed for statistics?, Equivalences between learning of data and probability distributions, and their applications, Characterizing the continuous degrees, The random members of a \({\Pi }_{1}^{0}\) class, Algorithmic tests and randomness with respect to a class of measures, ON A METRIC GENERALIZATION OF THE tt-DEGREES AND EFFECTIVE DIMENSION THEORY, Mass problems associated with effectively closed sets, MARTIN-LÖF RANDOMNESS IN SPACES OF CLOSED SETS, Measures and their random reals, Effective randomness for continuous measures, Cone avoidance and randomness preservation, Point Degree Spectra of Represented Spaces, Computability of Subsets of Metric Spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Effectively closed sets of measures and randomness
• Computability of probability measures and Martin-Löf randomness over metric spaces
• Uniform test of algorithmic randomness over a general space
• A generalization of Brouwer's fixed point theorem
• Algorithmic Randomness and Complexity
• Measures and their random reals
• Degrees of unsolvability of continuous functions
• THE COMPLEXITY OF FINITE OBJECTS AND THE DEVELOPMENT OF THE CONCEPTS OF INFORMATION AND RANDOMNESS BY MEANS OF THE THEORY OF ALGORITHMS
• Arithmetical Reducibilities I
• The definition of random sequences
• ∏ 0 1 Classes and Degrees of Theories
• On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction