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On the product of vector measures
| Content Provider | Scilit |
|---|---|
| Author | Kluvánek, Igor |
| Copyright Year | 1973 |
| Description | Let μ and ν be measures defined on some σ-algebrs with values in locally convex topological vector spaces X and Y, repectively. It is possible [1] to construct their product λ = μ × ν as a measure on a σ-algebra if λ is allowed to take its values in X $⊗_{ε}$ Y, the completion of X ⊗ Y in the topology of bi-equicontinuous convergence. The reason is, roughly speaking, that the topology of biequicontinuous convergence on X ⊗ Y is coarse enough to make λ σ-additive and the completion X $⊗_{ε}$ Y is big enough to accommodate all values of λ. Here we are going to improve the result by introducing a finer topology on X ⊗ Y in which λ will be σ-additive and such that all values of λ will belong to the completion of X ⊗ Y under that topology. The topology in question is obtained by a slight modification from a topology considered for the first time in the work [3] of Jacobs. Curiously enough, the proof of the improved result is simpler than that of [1] and reduces almost to a direct observation avoiding duality arguments. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A547BCDD407E5EBCC705CE26DC02148D/S1446788700012714a.pdf/div-class-title-on-the-product-of-vector-measures-div.pdf |
| Ending Page | 26 |
| Page Count | 5 |
| Starting Page | 22 |
| ISSN | 00049735 |
| DOI | 10.1017/s1446788700012714 |
| Journal | Journal of the Australian Mathematical Society |
| Issue Number | 1 |
| Volume Number | 15 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1973-02-01 |
| Access Restriction | Open |
| Subject Keyword | Journal of the Australian Mathematical Society Applied Mathematics Completion of X |
| Content Type | Text |
| Resource Type | Article |
