Measures and Tensors II

Lamadrid, Jesús Gil de

Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 762-793

Résumé

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.

Détail

DOI : 10.4153/CJM-1966-077-3

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