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Local integral metrics and Daniell-Loomis integrals

Published online by Cambridge University Press:  17 April 2009

M. Diaz Carrillo  and
H. Günzler
M. Diaz Carrillo
Affiliation:
Dpto Analisis Matematico, Universidad de Granada, Granada, Spain
H. Günzler
Affiliation:
Mathematisches Seminar Der Christian-Albrechts-Universität Kiel, Germany
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Recently Guerrero and the first author (Diaz Carrillo) proved an anologue to Daniell's extension process which works for arbitrary nonnegative linear functionals, without any continuity conditions. With the aid of Schäfke's local integral metrics we generalise this extension process and prove convergence theorems using a suitable local mean convergence, which can be traced back to Loomis.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 3 , December 1993 , pp. 411 - 426
Copyright
Copyright © Australian Mathematical Society 1993

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