Citation
Mitsis, Themistoklis (1998) On a Problem in Geometric Measure Theory Related to Sphere and Circle Packing. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/992h-9263. https://resolver.caltech.edu/CaltechTHESIS:08012025-171149569
Abstract
In this thesis we prove that a Borel set which contains spheres centered at all points of a Borel set of Hausdorff dimension greater than 1 must have positive Lebesgue measure, and, using the same method, we rederive a special case of Stein's spherical means maximal inequality. We also prove the corresponding result for circles, provided that the set of centers has Hausdorff dimension greater than 3/2.
| Item Type: | Thesis (Dissertation (Ph.D.)) | ||||
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| Subject Keywords: | (Mathematics) | ||||
| Degree Grantor: | California Institute of Technology | ||||
| Division: | Physics, Mathematics and Astronomy | ||||
| Major Option: | Mathematics | ||||
| Thesis Availability: | Public (worldwide access) | ||||
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| Thesis Committee: |
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| Defense Date: | 16 March 1998 | ||||
| Record Number: | CaltechTHESIS:08012025-171149569 | ||||
| Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:08012025-171149569 | ||||
| DOI: | 10.7907/992h-9263 | ||||
| ORCID: |
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| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||
| ID Code: | 17583 | ||||
| Collection: | CaltechTHESIS | ||||
| Deposited By: | Benjamin Perez | ||||
| Deposited On: | 04 Aug 2025 23:08 | ||||
| Last Modified: | 04 Aug 2025 23:18 |
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