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Which measures are projections of purely unrectifiable one-dimensional Hausdorff measures. (English) Zbl 1167.28002

The authors present a necessary and sufficient condition for a measure \(\mu\) on the real line to be an orthogonal projection of \({\mathcal H}^1_A\) for some purely 1-unrectifiable planar set \(A\). In particular, they answer a question of D. Preiss.

MSC:

28A78 Hausdorff and packing measures
28A80 Fractals
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References:

[1] K. J. Falconer, The geometry of fractal sets, Cambridge Tracts in Mathematics, vol. 85, Cambridge University Press, Cambridge, 1986. · Zbl 0587.28004
[2] Pertti Mattila, Geometry of sets and measures in Euclidean spaces, Cambridge Studies in Advanced Mathematics, vol. 44, Cambridge University Press, Cambridge, 1995. Fractals and rectifiability. · Zbl 0819.28004
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