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Questions about Hausdorff measures, their variants (such as spherical Hausdorff measures) and generalisations.

12 votes
2 answers
790 views

Sets that project to zero measure on all lines except one

It is a (difficult) exercise to show that there exists a measurable set $E \subset [0,1]^2$ (necessarily with zero 2-dimensional Lebesgue measure) such that the projection on every line passing throug …