Computable Measure Theory and Algorithmic Randomness

DOI10.1007/978-3-030-59234-9_7OpenAlexW3085512952MaRDI QIDQ5024573

Publication date: 26 January 2022

Published in: Theory and Applications of Computability (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/hal-02938919/file/Chapter_HR.pdf

Mathematics Subject Classification ID

Computation over the reals, computable analysis (03D78)

Cites Work

Randomness on computable probability spaces - A dynamical point of view
On the computability of a construction of Brownian motion
Algorithmic randomness over general spaces
The Law of the Iterated Logarithm for Algorithmically Random Brownian Motion
Algorithmic Randomness of Closed Sets
A constructive view on ergodic theorems
MARTIN-LÖF RANDOMNESS IN SPACES OF CLOSED SETS
The definition of random sequences
Van Lambalgen's theorem for uniformly relative Schnorr and computable randomness
Kolmogorov complexity and the geometry of Brownian motion
An introduction to Kolmogorov complexity and its applications
An example of a computable absolutely normal number
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When does randomness come from randomness?
A constructive version of Birkhoff's ergodic theorem for Martin-Löf random points
Conditional measure and the violation of van Lambalgen's theorem for Martin-Löf randomness
Randomness on computable probability spaces -- a dynamical point of view
Algorithmic randomness and monotone complexity on product space
Dynamics and abstract computability: computing invariant measures
Algorithmic randomness, reverse mathematics, and the dominated convergence theorem
Computable de Finetti measures
Computability of measurable sets via effective topologies
Are unbounded linear operators computable on the average for Gaussian measures?
Upcrossing inequalities for stationary sequences and applications
On a definition of random sequences with respect to conditional probability
Infinite subsets of random sets of integers
A constructive Borel-Cantelli lemma. Constructing orbits with required statistical properties
A computable approach to measure and integration theory
Effective symbolic dynamics, random points, statistical behavior, complexity and entropy
The computational complexity of maximization and integration
Use of the Kolmogorov complexity in analyzing control system dynamics
The speed of convergence in the ergodic theorem
Ergodic theorems for individual random sequences
Computability on random variables
Computability on the probability measures on the Borel sets of the unit interval
Nonrobustness property of the individual ergodic theorem
Random elements in effective topological spaces with measure.
The descriptive complexity of Brownian motion
Schnorr randomness for noncomputable measures
Uncomputably noisy ergodic limits
The Borel-Cantelli lemmas, probability laws and Kolmogorov complexity
Computability of the ergodic decomposition
Probabilistic computability and choice
Universality, optimality, and randomness deficiency
Computability of probability measures and Martin-Löf randomness over metric spaces
Statistical properties of dynamical systems -- Simulation and abstract computation
Dynamics of a generic Brownian motion: Recursive aspects
A computable version of the Daniell-Stone theorem on integration and linear functionals
Algorithmic tests and randomness with respect to a class of measures
Zufälligkeit und Wahrscheinlichkeit. Eine algorithmische Begründung der Wahrscheinlichkeitstheorie. (Randomness and probability. An algorithmic foundation of probability theory)
Uniform test of algorithmic randomness over a general space
Randomness and Non-ergodic Systems
Computable randomness and betting for computable probability spaces
Martin-Löf random points satisfy Birkhoff’s ergodic theorem for effectively closed sets
L1-Computability, Layerwise Computability and Solovay Reducibility
Schnorr randomness and the Lebesgue differentiation theorem
Representations of measurable sets in computable measure theory
The difference between optimality and universality
The dimension of ergodic random sequences
Fourier spectra of measures associated with algorithmically random Brownian motion
Probabilistic Constructions of Computable Objects and a Computable Version of Lovász Local Lemma
Algorithmic randomness for Doob's martingale convergence theorem in continuous time
On zeros of Martin-Löf random Brownian motion
Complexity Theory for Operators in Analysis
Las Vegas Computability and Algorithmic Randomness
Computability on measurable functions
Differentiability of polynomial time computable functions
Von Neumann's Biased Coin Revisited
Randomness and the Ergodic Decomposition
Computability of the Radon-Nikodym Derivative
The probability distribution as a computational resource for randomness testing
Algorithmic Randomness and Complexity
L p -Computability in Recursive Analysis
Local stability of ergodic averages
Randomness and differentiability
Members of Random Closed Sets
Fractals Generated by Algorithmically Random Brownian Motion
Computable Exchangeable Sequences Have Computable de Finetti Measures
An Application of Martin-Löf Randomness to Effective Probability Theory
Ergodic-Type Characterizations of Algorithmic Randomness
Applications of Effective Probability Theory to Martin-Löf Randomness
Von Mises' definition of random sequences reconsidered
The Law of the Iterated Logarithm for Random Kolmogorov, or Chaotic, Sequences
Эффективная сходимость по вероятности и эргодическая теорема для индивидуальных случайных последовательностей
On computability and disintegration
L^p‐Computability
Introduction to Dynamical Systems
On the Convergence of Fourier Series of Computable Lebesgue Integrable Functions
Effective Randomness for Computable Probability Measures
Random Continuous Functions
Arithmetical representations of Brownian motion I
Algorithmic Aspects of Lipschitz Functions
Computable Riesz representation for the dual of C [0; 1]
Admissible representations for probability measures
USING ALMOST-EVERYWHERE THEOREMS FROM ANALYSIS TO STUDY RANDOMNESS

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