Applications of fuzzy set theory and near vector spaces to functional analysis
| dc.contributor.author | Pinchuck, Andrew L. | |
| dc.date.accessioned | 2011-06-06T11:37:01Z | |
| dc.date.available | 2011-06-06T11:37:01Z | |
| dc.date.issued | 2011-06-06 | |
| dc.description.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. | en_US |
| dc.identifier.uri | http://hdl.handle.net/10539/10006 | |
| dc.language.iso | en | en_US |
| dc.title | Applications of fuzzy set theory and near vector spaces to functional analysis | en_US |
| dc.type | Thesis | en_US |