On the Discrepancy Function in Arbitary Dimension, Close to L ^{1}

Michael T Lacey

Let ${\mathcal{A}}_N$ to be $N$ points in the unit cube in dimension $d$, and consider the Discrepency function D_N(\vec x) \coloneqq \sharp \mathcal A_N \cap [\vec 0,\vec x)-N \abs{…