Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Supervisors info:
Τηλέμαχος Χατζηαφράτης, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Οι τύποι Area και Coarea στη Γεωμετρική Θεωρία Μέτρου
Translated title:
Area and Coarea formulas in Geometric Measure Theory
Summary:
In this master thesis we present and prove Area and Coarea formulas.
In introductory Chapter 1 the two formulas are stated along with representative examples. The wider proof procedure starts from Chapter 2 where the necessary background about Measure Theory is propounded. In Chapter 3 Hausdorff measures are introduced. Chapter 4 contains information regarding Lipschitz functions. Here we prove Rademacher's Theorem. Chapter 5 includes some basic linear algebra followed by more specific tools. In Chapter 6 we finally prove Area and Coarea formulas.
Main subject category:
Science
Keywords:
Area, Coarea, Geometric Measure Theory
