✦ LIBER ✦
A nonstandard density theorem for weak topologies on Banach and Bochner spaces
✍ Scribed by Laurent Vanderputten
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 165 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0044-3050
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✦ Synopsis
Abstract
We prove a nonstandard density result. It asserts that if a particular formula is true for functions in a set K of linear continuous functions between Banach spaces E and D, then it remains valid for functions that are limits, in the uniform convergence topology on a given class ℳ︁ of subsets of E, of nets of vectors in K. We then apply this result to various class ℳ︁ and sets__K__ in the context of E‐valued Bochner integrable functions defined on a finite measure space.