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

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.

### MSC:

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