Lebesgue measure of numbers whose decimal representation contains at least one digit equal $9$ Let $A$ be the set of numbers on $[0, 1]$ whose decimal representation contains at least one digit equal $9$. What is its Lebesgue measure $\lambda(A)$?

Recall that a real number is said to be normal (in base $10$) if every sequence of $n$ consecutive digits appears in its decimal expansion with frequency $1/10^n$.
In 1909 Borel proved that almost every real number (wrt the Lebesgue measure) is normal. In particular, this means that $\lambda(A) = \lambda([0,1]) = 1$.
