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A localic theory of lower and upper integrals

✍ Scribed by Steven Vickers

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
211 KB
Volume
54
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

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. (Β© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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