В оригинале всюду вместо Х было кси(греческая буква)
In English:
X=X1/3 + X2/9 +X3/27 + ...+Xk/3*k+...,
where Х1,Х2,...,Хk,... is a sequence of independent random variables, taking values 0 and 2 with probabilities 1/3 and 2/3
1) prove that X has a continuous distribution
2) prove that F (с индексом кси) is singularly continuons
3) calculate the lebesgue measure at the spectrum S(с индексом кси)