The purpose of this thesis is to examine certain questions concerning the Cantor ternary set. The second chapter deals with proving that the Cantor ternary set is equivalent to the middle thirds set of [0,1], closed, compact, and has Lebesgue measure zero. Further a proof that the Cantor ternary set is a locally compact, Hausdorff topological group is given. The third chapter is concerned with establishing the existence of a Haar integral on certain topological groups. In particular if G is a locally compact and Hausdorff topological group, then there is a non-zero translation invariant positive linear form on G. The fourth chapter deals with proving that for any Haar integral I on G there exists a unique Haar measure on G that represents I.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc504018 |
| Date | 08 1900 |
| Creators | Naughton, Gerard P. (Gerard Peter) |
| Contributors | Lewis, Paul Weldon, Brand, Neal E. |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iii, 77 leaves, Text |
| Rights | Public, Naughton, Gerard P. (Gerard Peter), Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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