A typical number is extremely non-normal

Anastasios Stylianou

Fix a positive integer $N\ge 2$. For a real number $x\in [0,1]$ and a digit $i\in \{0,1,...,N-1\}$, let ${\Pi }_i(x,n)$ denote the frequency of the digit $i$ among the first $n$ $N$-adi…