A computational model for metric spaces
Theoretical Computer Science
Computability on random variables
Theoretical Computer Science - Special issue on computability and complexity in analysis
Effective properties of sets and functions in metric spaces with computability structure
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
Random elements in effective topological spaces with measure
Information and Computation
Computability on subsets of metric spaces
Theoretical Computer Science - Topology in computer science
Mathematical Structures in Computer Science
A computable version of the Daniell-Stone theorem on integration and linear functionals
Theoretical Computer Science
Uniform test of algorithmic randomness over a general space
Theoretical Computer Science
A computable approach to measure and integration theory
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Computability of probability measures and Martin-Löf randomness over metric spaces
Information and Computation
Applications of Effective Probability Theory to Martin-Löf Randomness
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
A constructive version of Birkhoff's ergodic theorem for Martin-Löf random points
Information and Computation
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In this paper we provide a framework for computable analysis of measure, probability and integration theories. We work on computable metric spaces with computable Borel probability measures. We introduce and study the framework of layerwise computability which lies on Martin-Löf randomness and the existence of a universal randomness test. We then prove characterizations of effective notions of measurability and integrability in terms of layerwise computability. On the one hand it gives a simple way of handling effective measure theory, on the other hand it provides powerful tools to study Martin-Löf randomness, as illustrated in a sequel paper.