Geodesic
Extension of a Bounded Vector Measure with Values in a ReflexiveBanach Space
Canadian mathematical bulletin, Tome 10 (1967) no. 4, pp. 525-529

Voir la notice de l'article provenant de la source Cambridge University Press

A vector measure (countable additive set function with values in a Banachspace) on a field may be extended to a vector measure on the generated σ-field, under certain hypotheses. For example, the extension is establishedfor the bounded variation case [2, 5, 8], and there are more generalconditions under which the extension exists [ 1 ]. The above results have ashypotheses fairly strong boundedness conditions on the n o rm of the measureto be extended. In this paper we prove an extension theorem of the same typewith a restriction on the range, supposing further that the measure ismerely bounded. In fact a vector measure on a σ- field is bounded (III. 4. 5of [3]) but it is conceivable that a vector measure on a field could beunbounded. 
Fox, Geoffrey. Extension of a Bounded Vector Measure with Values in a ReflexiveBanach Space. Canadian mathematical bulletin, Tome 10 (1967) no. 4, pp. 525-529. doi: 10.4153/CMB-1967-052-1
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