Let $z_1,z_2,\dots \in [0,1]$ be an infinite sequence, and define the discrepancy$$D_N(I)=\#\{n\le N:z_n\in I\}-N|I|.$$Must there exist some interval $I\subseteq [0,1]$ such that$$\underset{N\to \infty }{\mathrm{limsup}}|D_N(I)|=\infty ?$$