Applications of fuzzy set theory and near vector spaces to functional analysis
Date
2011-06-06
Authors
Pinchuck, Andrew L.
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Abstract
We prove an original version of the Hahn-Banach theorem in the fuzzy setting. Convex
compact sets occur naturally in set-valued analysis. A question that has not been
satisfactorily dealt with in the literature is: What is the relationship between collections
of such sets and vector spaces? We thoroughly clarify this situation by making use of
R°adstr ¨om’s embedding theorem, leading up to the definition of a near vector space. We
then go on to successfully apply these results to provide an original method of proof of
Doob’s decomposition of submartingales.