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

Abstract

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.

Citation

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

Information

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

zbMATH: 1384.28006
MathSciNet: MR3365390

Subjects:
Primary: 28A12
Secondary: 28A75 , 28A80

Keywords: Baire category , tangent measures

Rights: Copyright © 2015 Michigan State University Press

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