Fractal dimension of the intersection of standard Cantor sets (Q1397574)

For a standard Cantor set \(K\), the author shows that for almost all \(a\in[0,1]\), the Hausdorff dimension of \(K\cap(K+a)\) is not greater than \(3^{-1}\log 2/\log 3\). The latter number is strictly smaller than \(\log 4/\log 3-1\), which would be the case if the co-dimension of the intersection of two fractal sets almost always equals the sum of the co-dimensions of the individual sets.