Domain Theory and Integration (1995)
| Venue: | Theoretical Computer Science |
| Citations: | 56 - 11 self |
BibTeX
@ARTICLE{Edalat95domaintheory,
author = {Abbas Edalat},
title = {Domain Theory and Integration},
journal = {Theoretical Computer Science},
year = {1995},
volume = {151},
pages = {163--193}
}
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Abstract
We present a domain-theoretic framework for measure theory and integration of bounded real-valued functions with respect to bounded Borel measures on compact metric spaces. The set of normalised Borel measures of the metric space can be embedded into the maximal elements of the normalised probabilistic power domain of its upper space. Any bounded Borel measure on the compact metric space can then be obtained as the least upper bound of an !-chain of linear combinations of point valuations (simple valuations) on the upper space, thus providing a constructive setup for these measures. We use this setting to define a new notion of integral of a bounded real-valued function with respect to a bounded Borel measure on a compact metric space. By using an !-chain of simple valuations, whose lub is the given Borel measure, we can then obtain increasingly better approximations to the value of the integral, similar to the way the Riemann integral is obtained in calculus by using step functions. ...
