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On The Extension Of Measure By The Method Of Borel

Published online by Cambridge University Press:  20 November 2018

L. LeBlanc  and
G. E. Fox
L. LeBlanc
Affiliation:
Université de Montréal
G. E. Fox
Affiliation:
Université de Montréal
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Introduction. This paper concerns the problem of extending a given measure defined on a Boolean ring to a measure on the generated σ-ring. Two general methods are familiar to the literature, that of Lebesgue (outer measure) and a method proposed by Borel using transfinite induction (4, 49-134; 2, 228-238).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 516 - 523
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Albuquerque, J., Ensembles de Borel, Portugaha Math. (1944).Google Scholar
2. Borel, E., Leçons sur la théorie des fonctions. Collection de monographies sur la théorie des fonctions publiées sous la direction de Emile Borel (Paris, ).Google Scholar
3. Halmos, P. R., Measure Theory (New York, 1950).Google Scholar
4. Lusin, N., Leçons sur les ensembles analytiques et leurs applications. Collection de monographies sur la théorie des fonctions publiées sous la direction de Emile Borel (Paris, 1930).Google Scholar
5. Neves, R., Söbre a construçae algebrica da teoria gérai da Medida. Instituto Para a alta cultura, Gendro de estudas matematicas, Publ. no. 13, 22 pp. (1945).Google Scholar