Geodesic
Non-Averaging Sets, Dimension and Porosity
Canadian mathematical bulletin, Tome 29 (1986) no. 1, pp. 60-63

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DOI

A subset of the line is called non-averaging if, whenever two points belong to the set, their average does not. This paper provides an example of a closed set which is small in the sense that it is non-averaging and has porosity 1 at each of its points and yet large in the sense that its Hausdorff dimension is 1.
DOI : 10.4153/CMB-1986-011-2
Mots-clés : 26A21, 28A05 
Foran, James. Non-Averaging Sets, Dimension and Porosity. Canadian mathematical bulletin, Tome 29 (1986) no. 1, pp. 60-63. doi: 10.4153/CMB-1986-011-2
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     title = {Non-Averaging {Sets,} {Dimension} and {Porosity}},
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     doi = {10.4153/CMB-1986-011-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-011-2/}
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