[CvGmt News] [cvgmt seminar] Besicovitch-Federer projection theorem is false in every infinite dimensional Banach space

ambrosio at sns.it ambrosio at sns.it
Tue May 8 07:52:10 CEST 2018


Besicovitch-Federer projection theorem is false in every infinite dimensional Banach space
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http://cvgmt.sns.it/seminar/640/

Date: Monday, May 14, 2018

Time: 11:00

Place: Scuola Normale Superiore, Aula Marie Curie

Speaker: David Bate



Abstract. The Besicovitch-Federer projection theorem is a fundamental result of classical geometric measure theory and it is natural to ask if generalisations exist outside of the Euclidean setting.  We will demonstrate its failure in Hilbert space by constructing a purely unrectifiable set of finite $\mathcal H^1$ measure whose image under every (non-zero) continuous linear function has positive Lebesgue measure.  Time permitting, I will discuss how the counter example may be generalised to any infinite dimensional separable Banach space.  This is joint work with Marianna Csörnyei and Bobby Wilson.



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