# Question: a find the lebesgue measure of the set of real...

###### Question details

a) Find the Lebesgue measure of the set of real numbers x ∈ [0, 1] which can be written in base 3 as x = 0.x1x2x3 · · · with xk= 1 whenever k = n^2 for some n ∈ Z +

b) estimate the measure of the set of real numbers x ∈ [0, 1] which can be written in base 3 as x = 0.x1x2x3 · · · such that for all n ∈ Z + we do not have xk = 1 for all (n−1)^2 < k ≤ n^2