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A localic theory of lower and upper integrals

Vickers, Steven (2008) A localic theory of lower and upper integrals. Mathematical Logic Quarterly, 54 (4). pp. 109-123. ISSN 0942-5616

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URL of Published Version: http://www3.interscience.wiley.com/journal/117902848/abstract

Identification Number/DOI: 10.1002/malq.200710028

An account of lower and upper integration is given. It is constructive in the sense of geometric logic. If the integrand takes its values in the non-negative lower reals, then its lower integral with respect to a valuation is a lower real. If the integrand takes its values in the non-negative upper reals,then its upper integral with respect to a covaluation and with domain of
integration bounded by a compact subspace is an upper real. Spaces of valuations and of covaluations are defined.

Riemann and Choquet integrals can be calculated in terms of these lower and upper integrals.

Type of Work:Article
Date:30 January 2008 (Publication)
School/Faculty:Schools (1998 to 2008) > School of Computer Science
Department:Computer Science
Subjects:Q Science (General)
QA Mathematics
Institution:University of Birmingham
Copyright Holders:John Wiley & Sons
ID Code:185
Refereed:YES
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