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The Riesz Representation Theorem and Extension of Vector Valued Additive Measures
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bongiorno, Benedetto Dinculeanu, Nicolae |
| Copyright Year | 2001 |
| Abstract | Let E F G be tree Banach spaces with E ⊂ L F G continuously, and let m → E be a finitely additive measure with finite semivariation, defined on a δ-ring of subsets of a given set S. A theory of integration of vector-valued functions f S → E, applicable to the stochastic integration in Banach spaces, is developed in [6, Sect. 5]. Many times a measure m is defined on a ring (rather than on a δring). In order to apply the above integration theory, we have to extend the measure m to a finitely additive measure on the δ-ring generated by . Extensions of finitely additive measures have not been considered so far in the literature. In Section 3 we prove such extension theorems (Theorems 3.6 and 3.7). In Theorem 3.8 and Corollary 3.9 we give conditions under which the extended measure is σ-additive. A particular case of |
| Starting Page | 706 |
| Ending Page | 732 |
| Page Count | 27 |
| File Format | PDF HTM / HTML |
| DOI | 10.1006/jmaa.2001.7569 |
| Volume Number | 261 |
| Alternate Webpage(s) | https://core.ac.uk/download/pdf/82577650.pdf |
| Alternate Webpage(s) | https://doi.org/10.1006/jmaa.2001.7569 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
