カントール分布
カントール分布の台はカントール集合、つまり(可算個の)集合
C 0 = [ 0 , 1 ] C 1 = [ 0 , 1 3 ] ∪ [ 2 3 , 1 ] C 2 = [ 0 , 1 9 ] ∪ [ 2 9 , 1 3 ] ∪ [ 2 3 , 7 9 ] ∪ [ 8 9 , 1 ] C 3 = [ 0 , 1 27 ] ∪ [ 2 27 , 1 9 ] ∪ [ 2 9 , 7 27 ] ∪ [ 8 27 , 1 3 ] ∪ [ 2 3 , 19 27 ] ∪ [ 20 27 , 7 9 ] ∪ [ 8 9 , 25 27 ] ∪ [ 26 27 , 1 ] C 4 = ⋯ {\displaystyle {\begin{aligned}C_{0}=&[0,1]\\C_{1}=&[0,{\tfrac {1}{3}}]\cup [{\tfrac {2}{3}},1]\\C_{2}=&[0,{\tfrac {1}{9}}]\cup [{\tfrac {2}{9}},{\tfrac {1}{3}}]\cup [{\tfrac {2}{3}},{\tfrac {7}{9}}]\cup [{\tfrac {8}{9}},1]\\C_{3}=&[0,{\tfrac {1}{27}}]\cup [{\tfrac {2}{27}},{\tfrac {1}{9}}]\cup [{\tfrac {2}{9}},{\tfrac {7}{27}}]\cup [{\tfrac {8}{27}},{\tfrac {1}{3}}]\cup \\&[{\tfrac {2}{3}},{\tfrac {19}{27}}]\cup [{\tfrac {20}{27}},{\tfrac {7}{9}}]\cup [{\tfrac {8}{9}},{\tfrac {25}{27}}]\cup [{\tfrac {26}{27}},1]\\C_{4}=&\cdots \end{aligned}}}