Extension of a Bounded Vector Measure with Values in a ReflexiveBanach Space
Canadian mathematical bulletin, Tome 10 (1967) no. 4, pp. 525-529
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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
@article{10_4153_CMB_1967_052_1,
author = {Fox, Geoffrey},
title = {Extension of a {Bounded} {Vector} {Measure} with {Values} in a {ReflexiveBanach} {Space}},
journal = {Canadian mathematical bulletin},
pages = {525--529},
year = {1967},
volume = {10},
number = {4},
doi = {10.4153/CMB-1967-052-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-052-1/}
}
TY - JOUR AU - Fox, Geoffrey TI - Extension of a Bounded Vector Measure with Values in a ReflexiveBanach Space JO - Canadian mathematical bulletin PY - 1967 SP - 525 EP - 529 VL - 10 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-052-1/ DO - 10.4153/CMB-1967-052-1 ID - 10_4153_CMB_1967_052_1 ER -
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