We continue our study of tangent measures by discussing two important results. The first is the succinctly titled theorem Tangent Measures of Tangent Measures are Tangent Measures. The second is a theorem of Preiss, which says measures whose densities exist must only have flat tangent measures almost everywhere.
- Notes (Alternatively read Section 2 of this paper by Kenig, Preiss and Toro.)
- Videos: Metrics on Measures, Tangent Measures of Tangent Measures are Tangent Measures, Cones, Densities imply Flat Tangent Measures.
- Exercises and Partial Solutions (prepare 2,4,5 and 6).