Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-21T10:12:38.305Z Has data issue: false hasContentIssue false

Abstract Daniell-Loomis spaces

Published online by Cambridge University Press:  17 April 2009

M. Díaz Carrillo
Affiliation:
Departamento de Análisis Matemático, Universidad de Granada, Granada 18071Spain
H. Günzler
Affiliation:
Mathematisches Seminar, Universitát Kiel, D 24098 KielGermany
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [3] for general integral metric q an integral extension of Lebesgue power was discussed. In this paper we introduce the abstract Daniell-Loomis spaces Rp, p real, 0 < p < ∞, of q-measurable functions with finite “p-norm”, and study their basic properties.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Anger, B. and Portenier, C., Randon integral (Birkhäuser, Basel, 1992).Google Scholar
[2]Bourbaki, N., Intégration. Elements de Mathematique XIII, Livre VI (Hermann, Paris, 1952).Google Scholar
[3]Carrillo, M. Díaz and Günzler, H., ‘Local integral metrics and Daniell-Loomis integrals’, Bull. Austral. Math. Soc. 48 (1993), 411426.Google Scholar
[4]Carrillo, M. Díaz and Rivas, P. Munoz, ‘Positive linear functionals and improper integration’, Ann. Sci. Math. Québec 18 (1994), 149157.Google Scholar
[5]Dunford, N. and Schwartz, J.T., Linear operators I (Interscience, New York, 1957).Google Scholar
[6]Gould, G.G., ‘The Daniell-Bourbaki integral for finitely additive measures’, Proc. London Math. Soc. 16 (1966), 297–230.Google Scholar
[7]Günzler, H., Integration (Bibliogr. Institut, Mannheim, 1985).Google Scholar
[8]König, H., ‘Daniell-Stone integration without the lattice condition and its application to uniform algebras’, Ann. Univ. Sarav. Ser. Math. 4 (1992).Google Scholar
[9]Loomis, L.H., ‘Linear functionals and content’, Amer. J. Math. 76 (1956), 168182.CrossRefGoogle Scholar
[10]Schäfke, F.W., ‘Integrationstheorie I’, J. Reine Angew. Math. 244 (1970), 154176.Google Scholar