• Publications
  • Influence
Computability of probability measures and Martin-Löf randomness over metric spaces
TLDR
In this paper, we investigate algorithmic randomness on more general spaces than the Cantor space in a computable and measure-theoretic sense. Expand
  • 112
  • 10
  • PDF
Randomness on Computable Probability Spaces—A Dynamical Point of View
TLDR
We extend Schnorr randomness (in the version introduced by Schnorr) to computable probability spaces and compare it to a dynamical notion of randomness: typicality. Expand
  • 48
  • 7
  • PDF
Applications of Effective Probability Theory to Martin-Löf Randomness
TLDR
We pursue the study of the framework of layerwise computability introduced in a preceding paper and give three applications to Martin-Lof randomness. Expand
  • 30
  • 5
  • PDF
Schnorr randomness and the Lebesgue differentiation theorem
We exhibit a close correspondence between L1-computable functions and Schnorr tests. Using this correspondence, we prove that a point x ∈ [0, 1]d is Schnorr random if and only if the LebesgueExpand
  • 38
  • 4
  • PDF
Algorithmic tests and randomness with respect to a class of measures
TLDR
This paper offers some new results on randomness with respect to classes of measures, along with a didactic exposition of their context based on results that appeared elsewhere. Expand
  • 34
  • 3
  • PDF
An Application of Martin-Löf Randomness to Effective Probability Theory
TLDR
We introduce and study the framework of layerwise computability which lies on Martin-Lof randomness and the existence of a universal randomness test. Expand
  • 37
  • 3
  • PDF
Computing the speed of convergence of ergodic averages and pseudorandom points in computable dynamical systems
TLDR
A pseudorandom point in an ergodic dynamical system over a computable metric space is a point which is computable but its dynamics has the same statistical behavior as a typical point of the system. Expand
  • 15
  • 3
  • PDF
A constructive Borel-Cantelli lemma. Constructing orbits with required statistical properties
TLDR
In the general context of computable metric spaces and computable measures we prove a kind of constructive Borel-Cantelli lemma: given a sequence (constructive in some way) of sets A" i with effectively summable measures, there are computable points which are not contained in infinitely many A"i. Expand
  • 28
  • 2
  • PDF
Effective symbolic dynamics, random points, statistical behavior, complexity and entropy
TLDR
We introduce and compare some notions of complexity for orbits in dynamical systems and prove: (i) that the complexity of the orbits of random points equals the Kolmogorov-Sinai entropy of the system. Expand
  • 48
  • 1
  • PDF
Computability of the Radon-Nikodym Derivative
TLDR
We study the computational content of the Radon-Nokodym theorem from measure theory in the framework of the representation approach to computable analysis. Expand
  • 32
  • 1
  • PDF
...
1
2
3
4
5
...