Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Complexity theory of real functions
Complexity theory of real functions
Dynamical systems, measures, and fractals via domain theory
Information and Computation
Selected papers of the workshop on Topology and completion in semantics
A computational model for metric spaces
Theoretical Computer Science
A domain-theoretic approach to computability on the real line
Theoretical Computer Science - Special issue on real numbers and computers
Computability on the probability measures on the Borel sets of the unit interval
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
Foundation of a computable solid modelling
Theoretical Computer Science
Bisimulation for labelled Markov processes
Information and Computation - Special issue: LICS'97
Riemann and Edalat integration on domains
Theoretical Computer Science - Topology in computer science
Semi-pullbacks and bisimulation in categories of Markov processes
Mathematical Structures in Computer Science
Mathematical Structures 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
Von Neumann's Biased Coin Revisited
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Computability on random events and variables in a computable probability space
Theoretical Computer Science
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We introduce a computable framework for Lebesgue's measure and integration theory in the spirit of domain theory. For an effectively given second countable locally compact Hausdorff space and an effectively given finite Borel measure on the space, we define a recursive measurable set, which extends the corresponding notion due to S@?anin for the Lebesgue measure on the real line. We also introduce the stronger notion of a computable measurable set, where a measurable set is approximated from inside and outside by sequences of closed and open subsets, respectively. The more refined property of computable measurable sets give rise to the idea of partial measurable subsets, which naturally form a domain for measurable subsets. We then introduce interval-valued measurable functions and develop the notion of recursive and computable measurable functions using interval-valued simple functions. This leads us to the interval versions of the main results in classical measure theory. The Lebesgue integral is shown to be a continuous operator on the domain of interval-valued measurable functions and the interval-valued Lebesgue integral provides a computable framework for integration.