Open Access
2013/2014 Tangent Measures of Typical Measures
Tuomas Sahlsten
Real Anal. Exchange 40(1): 53-80 (2013/2014).


We prove that for a typical Radon measure \(\mu\) in \(\mathbb{R}^d\), every non-zero Radon measure is a tangent measure of \(\mu\) at \(\mu\)-almost every point. This was already shown by T. O’Neil in his Ph.D. thesis from 1994, but we provide a different self-contained proof for this fact. Moreover, we show that this result is sharp: for any non-zero measure we construct a point in its support where the set of tangent measures does not contain all non-zero measures. We also study a concept similar to tangent measures on trees, micromeasures, and show an analogous typical property for them.


Download Citation

Tuomas Sahlsten. "Tangent Measures of Typical Measures." Real Anal. Exchange 40 (1) 53 - 80, 2013/2014.


Published: 2013/2014
First available in Project Euclid: 1 July 2015

zbMATH: 1384.28006
MathSciNet: MR3365390

Primary: 28A12
Secondary: 28A75 , 28A80

Keywords: Baire category , tangent measures

Rights: Copyright © 2015 Michigan State University Press

Vol.40 • No. 1 • 2013/2014
Back to Top