In this paper, we study continuous functions with no finite or infinite one-sided derivative anywhere. In 1925, A. S. Beskovitch published an example of such a function. Since then we call them Beskovitch functions. This construction is presented in chapter 2, The example was simple enough to clear the doubts about the existence of Besicovitch functions. In 1932, S. Saks showed that the set of Besicovitch functions is only a meager set in C[0,1]. Thus the Baire category method for showing the existence of Besicovitch functions cannot be directly applied. A. P. Morse in 1938 constructed Besicovitch functions. In 1984, Maly revived the Baire category method by finding a non-empty compact subspace of (C[0,1], || • ||) with respect to which the set of Morse-Besicovitch functions is comeager.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc278627 |
| Date | 12 1900 |
| Creators | Lee, Jae S. (Jae Seung) |
| Contributors | Mauldin, R. Daniel, Jackson, Steve, 1957-, Urbański, Mariusz |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | v, 76 leaves : ill., Text |
| Rights | Public, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Lee, Jae S. (Jae Seung) |
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