Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-15T18:28:30.573Z Has data issue: false hasContentIssue false
  • English
  • Français

Inductive Extension of a Vector Measure Under a Convergence Condition

Published online by Cambridge University Press:  20 November 2018

Geoffrey Fox
Geoffrey Fox*
Affiliation:
Université de Montréal, Montréal, P.Q.
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.

Let μ be a vector measure (countably additive set function with values in a Banach space) on a field. If μ is of bounded variation, it extends to a vector measure on the generated σ-field (2; 5; 8). Arsene and Strătilă (1) have obtained a result, which when specialized somewhat in form and context, reads as follows: “A vector measure on a field, majorized in norm by a positive, finite, subadditive increasing set function defined on the generated σ-field, extends to a vector measure on the generated σ-field”.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1246 - 1255
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Arsene, Gr. and Strătilă, S., Prolongement des mesures vectorielles, Rev. Roumaine Math. Pures Appl. 10 (1965), 333–338.Google Scholar
2. Dinculeanu, N., Regular measures, Acta Sci. Math. (Szeged) 24 (1963), 236–243.Google Scholar
3. Dunford, N. and Schwartz, J., Linear operators. I (Interscience Publishers, New York, 1957).Google Scholar
4. Fox, G., Note on the Borel method of measure extension, Can. Math. Bull. 5 (1962), 285–296.Google Scholar
5. Gaina, S., Extension of vector measures with finite variation, Rev. Roumaine Math. Pures Appl. 8 (1963), 151–154.Google Scholar
6. Halmos, P. R., Measure theory (D. Van Nostrand, New York, 1950).10.1007/978-1-4684-9440-2CrossRefGoogle Scholar
7. Le Blanc, L. and Fox, G. E., On the extension of measure by the method of Borel, Can. J. Math. 8 (1956), 516–523.Google Scholar
8. Nicolescu, M., Mathematical analysis (Romanian), Vol. I l l (Technica, Bucharest, 1960).Google Scholar