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| dc.contributor.author | Nghaywi, Vanessa Pierre | |
| dc.date.accessioned | 2021-04-22T22:48:08Z | |
| dc.date.available | 2021-04-22T22:48:08Z | |
| dc.date.issued | 2018-06-27 | |
| dc.identifier.citation | Nghaywi, V. P. (2018). The area formula for the Hausdorff measure (Master's thesis, Notre Dame University-Louaize, Zouk Mosbeh, Lebanon). Retrieved from http://ir.ndu.edu.lb/123456789/1307 | en_US |
| dc.identifier.uri | http://ir.ndu.edu.lb/123456789/1307 | |
| dc.description | M.S. -- Faculty of Natural and Applied Sciences, Notre Dame University, Louaize, 2018; "A thesis submitted to the Faculty of Natural and Applied Sciences in partial fulfillment of the requirements for the degree of Master of Science in Mathematics"; Includes bibliographical references (leaf 68). | en_US |
| dc.description.abstract | In this thesis, we will prove a very important theorem in real analysis called The Area formula for the Hausdorff Measure. This theorem is an extension of the well known theorem the Change of variables formula for the Lebesgue measure. In this thesis, we will define the Hausdorff measure and prove some of its properties. We will also define Lipschitz functions and prove some of its properties also. Then, we continue the thesis by proving all the lemmas needed to finalize the proof of the Area formula for the Hausdorff measure. Finally, we finish this thesis by showing three applications of the Area formula. | en_US |
| dc.format.extent | 68 leaves : illustrations | |
| dc.language.iso | en | en_US |
| dc.publisher | Notre Dame University-Louaize | en_US |
| dc.rights | Attribution-NonCommercial-NoDerivs 3.0 United States | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/us/ | * |
| dc.subject.lcsh | Hausdorff measures | |
| dc.subject.lcsh | Variables (Mathematics) | |
| dc.subject.lcsh | Measure theory | |
| dc.subject.lcsh | Area measurement | |
| dc.title | The area formula for the Hausdorff measure | en_US |
| dc.type | Thesis | en_US |
| dc.rights.license | This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 United States License. (CC BY-NC 3.0 US) | |
| dc.contributor.supervisor | Merhej, Jessica, Ph.D. | en_US |
| dc.contributor.department | Notre Dame University-Louaize. Department of Mathematics and Statistics | en_US |
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