Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

A. Marchese

Lusin type theorems for Radon measures

created by marchese on 23 Nov 2015
modified on 13 Sep 2017

[BibTeX]

Rend. Semin. Mat. Univ. Padova

Inserted: 23 nov 2015
Last Updated: 13 sep 2017

Year: 2015

Abstract:

We add to the literature the following observation. If $\mu$ is a singular measure on $\mathbb{R}^n$ which assigns measure zero to every porous set and $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a Lipschitz function which is non-differentiable $\mu$-a.e. then for every $C^1$ function $g:\mathbb{R}^n\rightarrow\mathbb{R}$ there holds $\mu\{x\in\mathbb{R}^n: f(x)=g(x)\}=0.$ In other words the Lusin type approximation property of Lipschitz functions with $C^1$ functions does not hold with respect to a general Radon measure.

Keywords: Lipschitz functions, Lusin type approximation, Radon measure, Porous set


Download:

Credits | Cookie policy | HTML 5 | CSS 2.1