We extend the notion of microscopic sets introduced for subsets of the real line, to the case of subsets of a Banach space X. Then we introduce the Microscopic Drop Property for closed and convex subsets of X, and we eventually show that, when X is reflexive, it is equivalent to the usual Drop Property defined by D.N. Kutzarova.
Microscopic sets in a Banach space and characterizations of the Drop Property
MARTELLOTTI, Anna
2004
Abstract
We extend the notion of microscopic sets introduced for subsets of the real line, to the case of subsets of a Banach space X. Then we introduce the Microscopic Drop Property for closed and convex subsets of X, and we eventually show that, when X is reflexive, it is equivalent to the usual Drop Property defined by D.N. Kutzarova.File in questo prodotto:
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