Abstract
If a vector-valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector-valued function spaces with Helly's property and consider convegence of vector measures and best approximations in function spaces in this class.
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Kitahara, K., Okada, T. On Vector-Valued Function Spaces with Helly's Property. Analysis in Theory and Applications 17, 86–100 (2001). https://doi.org/10.1023/A:1015596717617
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DOI: https://doi.org/10.1023/A:1015596717617