Publicacions Matemàtiques

An example pertaining to the failure of the Besicovitch-Federer structure Theorem in Hilbert space

Thierry De Pauw

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We give an example, in the infinite dimensional separable Hilbert space, of a purely unrectifiable Borel set with finite nonzero one dimensional Hausdorff measure, whose projection is nonnegligible in a set of directions which is not Aronszajn null.

Article information

Source
Publ. Mat., Volume 61, Number 1 (2017), 153-173.

Dates
Received: 20 May 2014
First available in Project Euclid: 22 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.pm/1482375628

Digital Object Identifier
doi:10.5565/PUBLMAT_61117_06

Mathematical Reviews number (MathSciNet)
MR3590118

Zentralblatt MATH identifier
1359.28004

Subjects
Primary: 28A75: Length, area, volume, other geometric measure theory [See also 26B15, 49Q15] 28A80: Fractals [See also 37Fxx] 53C65: Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]

Keywords
Rectifiable set purely unrectifiable set Hilbert space Negligible set

Citation

De Pauw, Thierry. An example pertaining to the failure of the Besicovitch-Federer structure Theorem in Hilbert space. Publ. Mat. 61 (2017), no. 1, 153--173. doi:10.5565/PUBLMAT_61117_06. https://projecteuclid.org/euclid.pm/1482375628


Export citation