An Application of Martin-Löf Randomness to Effective Probability Theory

DOI10.1007/978-3-642-03073-4_27zbMath1268.03055OpenAlexW1580871327MaRDI QIDQ3576058

Cristobal Rojas, Mathieu Hoyrup

Publication date: 28 July 2010

Published in: Mathematical Theory and Computational Practice (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-03073-4_27

zbMATH Keywords

computable analysisalgorithmic randomnessLebesgue integrationuniversal testlayerwise computabilityeffective probability theory

Mathematics Subject Classification ID

Theory of numerations, effectively presented structures (03D45) Algorithmic randomness and dimension (03D32) Computation over the reals, computable analysis (03D78)

Related Items (20)

Computability of convergence rates in the ergodic theorem for Martin-Löf random points ⋮ When does randomness come from randomness? ⋮ The Intersection of Algorithmically Random Closed Sets and Effective Dimension ⋮ Inside the Muchnik degrees. I: Discontinuity, learnability and constructivism ⋮ Statistical properties of dynamical systems -- Simulation and abstract computation ⋮ On zeros of Martin-Löf random Brownian motion ⋮ Schnorr randomness for noncomputable measures ⋮ Layerwise computability and image randomness ⋮ A constructive version of Birkhoff's ergodic theorem for Martin-Löf random points ⋮ Constraints placed on random sequences by their compressibility ⋮ Pointwise complexity of the derivative of a computable function ⋮ On the computability of a construction of Brownian motion ⋮ ON ANALOGUES OF THE CHURCH–TURING THESIS IN ALGORITHMIC RANDOMNESS ⋮ Algorithmic randomness, reverse mathematics, and the dominated convergence theorem ⋮ Algorithmic tests and randomness with respect to a class of measures ⋮ Decomposing Borel functions using the Shore–Slaman join theorem ⋮ Schnorr randomness and the Lebesgue differentiation theorem ⋮ Unnamed Item ⋮ Computable Measure Theory and Algorithmic Randomness ⋮ Universality, optimality, and randomness deficiency

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• THE COMPLEXITY OF FINITE OBJECTS AND THE DEVELOPMENT OF THE CONCEPTS OF INFORMATION AND RANDOMNESS BY MEANS OF THE THEORY OF ALGORITHMS
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