Boundedness of the density normalised Jones' square function does not imply 1-rectifiability

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Martikainen , H & Orponen , T 2018 , ' Boundedness of the density normalised Jones' square function does not imply 1-rectifiability ' , Journal de Mathematiques Pures et Appliquées , vol. 110 , pp. 71-92 . https://doi.org/10.1016/j.matpur.2017.07.009

Title: Boundedness of the density normalised Jones' square function does not imply 1-rectifiability
Author: Martikainen, Henri; Orponen, Tuomas
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2018-02
Language: eng
Number of pages: 22
Belongs to series: Journal de Mathematiques Pures et Appliquées
ISSN: 0021-7824
URI: http://hdl.handle.net/10138/310807
Abstract: Recently, M. Badger and R. Schul proved [4] that for a 1-rectifiable Radon measure mu, the density weighted Jones' square function. (J) over tilde (2)(x) = Sigma(Q is an element of D) (l(Q) is finite for mu-a.e Answering a question of Badger Schul, we show that the converse is not true. Given epsilon > 0, we construct a Radon probability measure on [0,1](2) subset of R-2 with the properties that (J) over tilde (2)(x)
Subject: Beta numbers
Jones' square function
Rectifiability of measures
N-RECTIFIABILITY
TERMS
111 Mathematics
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