Schnorr randomness and the Lebesgue differentiation theorem

DOI10.1090/S0002-9939-2013-11710-7zbMath1307.03027MaRDI QIDQ2862195

Stephen G. Simpson, Noopur Pathak, Cristobal Rojas

Publication date: 14 November 2013

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

zbMATH Keywords

Lebesgue differentiation theoremSchnorr randomness

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Algorithmic randomness and dimension (03D32)

Related Items (13)

When does randomness come from randomness? ⋮ Randomness and differentiability ⋮ A Computational Approach to the Borwein-Ditor Theorem ⋮ USING ALMOST-EVERYWHERE THEOREMS FROM ANALYSIS TO STUDY RANDOMNESS ⋮ A NOTE ON THE LEARNING-THEORETIC CHARACTERIZATIONS OF RANDOMNESS AND CONVERGENCE ⋮ Schnorr randomness for noncomputable measures ⋮ Characterization of Kurtz randomness by a differentiation theorem ⋮ Lowness, Randomness, and Computable Analysis ⋮ Pointwise complexity of the derivative of a computable function ⋮ Algorithmic randomness and Fourier analysis ⋮ Computable randomness and betting for computable probability spaces ⋮ Martin-Löf random quantum states ⋮ Computable Measure Theory and Algorithmic Randomness

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• Martin-Löf random points satisfy Birkhoff’s ergodic theorem for effectively closed sets
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• Algorithmic Randomness and Complexity
• Local stability of ergodic averages
• Randomness and differentiability
• An Application of Martin-Löf Randomness to Effective Probability Theory

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