SUBJECT
Title
Geometric measure theory
Type of instruction
lecture + practical
Level
master
Faculty
Part of degree program
Credits
4+3
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Hausdorff measure, energy and capacity. Dimensions of product sets. Projection theorems.
Covering theorems of Vitali and Besicovitch. Differentiation of measures.
The Kakeya problem, Besicovitch set, Nikodym set.
Dini derivatives. Contingent. Denjoy-Young-Saks theorem.
Readings
- P. Mattila: Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability. Cambridge University Press, Cambridge, 1995.
- K. Falconer: Geomerty of Fractal Sets, Cambridge University Press, Cambridge, 1986.
- S. Saks: Theory of the Integral, Dover, 1964