An L^1 estimate for half-space discrepancy

William W. L. Chen, Giancarlo Travaglini

For every unit vector $\sigma \in {\Sigma }_{d-1}$ and every $r\ge 0$, let % % \begin{displaymath} P_{σ,r}=[-1,1]^d\cap\{t\in\Rr^d:t\cdotσ\le r\} \end{displaymath} % % denote the intersection of t…