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Measures and Tensors II

Published online by Cambridge University Press:  20 November 2018

Jesús Gil de Lamadrid
Jesús Gil de Lamadrid*
Affiliation:
University of Minnesota, Minneapolis, Minnesota and Centre Universitaire International, Paris
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The present work is a sequel to our previous article (10) with the same title. The major theme remains the study of the relationship between tensor products of spaces of functions and vector-valued measures on a space S. In (10) S was a compact Hausdorff space. Here we extend our considerations to locally compact Hausdorff spaces. B(S) still stands for the Borel class of S.

Three types of vector-valued measures m : B(5) → E, E a Banach space, are considered here (§3), namely, weak*, weak, and strong vector measures, but the concepts of weak and strong measures coincide. This result is due to Bartle, Dunford, and Schwartz (1) for abstract vector measures, i.e. defined on an abstract σ-algebra of sets.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 762 - 793
Copyright
Copyright © Canadian Mathematical Society 1966

References

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