Document Zbl 1359.28004

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An example pertaining to the failure of the Besicovitch-Federer structure theorem in Hilbert space. (English) Zbl 1359.28004

Publ. Mat., Barc. 61, No. 1, 153-173 (2017).

Summary: 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.

Cited in 1 Review

Cited in 2 Documents

MSC:

28A75	Length, area, volume, other geometric measure theory
28A80	Fractals
53C65	Integral geometry

Keywords:

rectifiable set; purely unrectifiable set; Hilbert space; negligible set

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