Analysis Learning Seminar
An Introduction to Rectifiable Sets and Measures
Lisa Naples (University of Connecticut)
Friday, March 23, 2018
Geometric Measure Theory uses measure theoretic techniques to classify structural properties of sets. A set in Euclidean space can be classified by its Hausdorff dimension, but even sets of a fixed dimension can have drastically different structures.
In this talk I will introduce the notion of rectifiability as a structural property of sets, and describe a classification theorem for rectifiable sets of integer dimension. I will end by discussing some more recent extensions to rectifiability of measures.