Almost everywhere continuous functions
| dc.contributor.author | Johnson, Kermit Gene | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2019-07-03T20:52:12Z | en |
| dc.date.available | 2019-07-03T20:52:12Z | en |
| dc.date.issued | 1967 | en |
| dc.description.abstract | Let X be a locally compact σ compact Hausdorff space. Let µ be a complete regular Borel measure defined on the Borel sets of X. It is shown that there is a base for the topology of X consisting of open sets whose boundaries are of µ measure zero. Let (S, p) be a metric space. It is shown that a function on X whose range is a subset of S can be uniformly approximated by µ almost everywhere continuous simple functions if, and only if, the function itself is µ almost everywhere continuous and its range is a totally bounded subset of S. S is then specialized to be a Banach algebra and several consequences are obtained culminating in the study of the ideal structure of the ring of ail µ almost everywhere continuous functions on X whose ranges are totally bounded subsets of a Banach algebra which is either the reals, complexes or quaternions. | en |
| dc.description.degree | Ph. D. | en |
| dc.format.extent | 32 leaves | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.uri | http://hdl.handle.net/10919/91174 | en |
| dc.language.iso | en | en |
| dc.publisher | Virginia Polytechnic Institute | en |
| dc.relation.isformatof | OCLC# 40834229 | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.lcc | LD5655.V856 1967.J62 | en |
| dc.title | Almost everywhere continuous functions | en |
| dc.type | Dissertation | en |
| dc.type.dcmitype | Text | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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