Abstract
We show that for every ɛ > 0 there is a set A ⊂ ℝ3 such that H 1 ⌞A is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and H 1 ⌞A has the 1-dimensional density between 1 and 2+ɛ everywhere in the support.
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Research of the first and the third author is supported by the grant MSM 0021620839.
Research of the second author is supported by the grant AV 0Z 10190503.
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Černý, R., Kolář, J. & Rokyta, M. Concentrated monotone measures with non-unique tangential behavior in ℝ3 . Czech Math J 61, 1141–1167 (2011). https://doi.org/10.1007/s10587-011-0054-6
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DOI: https://doi.org/10.1007/s10587-011-0054-6