Lecturer: Matthew Hyde
Term(s): Term 1
Commitment: 30 lectures
Assessment: Oral exam
Prerequisites: Familiarity with topics covered in Analysis I, II & III and MA260: Norms, metrics and topologies.
The first part of this course provides an introduction of measure theory for students of all mathematical backgrounds. We will adopt a more advanced approach than a standard undergraduate module, so there will be new content even for those students who have taken measure theory before. This will cover:
- Measures, Carathéodory's construction, integration and convergence theorems.
- Riesz representation theorem, weak* convergence and Prokhorov's theorem.
- Hardy-Littlewood maximal inequality and Rademacher’s theorem.
The second part provides an introduction to geometric measure theory. Time permitting, we will cover some of the following topics:
- Hausdorff distance.
- Hausdorff measure, rectifiable and purely unrectifiable sets.
- Sard's theorem.
- The Besicovitch projection theorem.
Course notes can be found on the Moodle page.
- Rudin, W.: Real and Complex Analysis
- Federer, H.: Geometric measure theory
- Mattila, P.: Geometry of Sets and Measures in Euclidean Spaces