Displaying similar documents to “A note on the three-segment problem”

Concentrated monotone measures with non-unique tangential behavior in ℝ 3

Robert Černý, Jan Kolář, Mirko Rokyta (2011)

Czechoslovak Mathematical Journal

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We show that for every ε > 0 there is a set A ⊂ ℝ 3 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 + ε everywhere in the support.

Monotone measures with bad tangential behavior in the plane

Robert Černý, Jan Kolář, Mirko Rokyta (2011)

Commentationes Mathematicae Universitatis Carolinae

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We show that for every ε > 0 , there is a set A ⊂ ℝ 2 such that ℋ 1 ⌞ A is a monotone measure, the corresponding tangent measures at the origin are not unique and ℋ 1 ⌞ A has the 1 -dimensional density between 1 and 3 + ε everywhere on the support.