Another measure of discrepancy for numeric sequences is the star discrepancy D∗ N , which is equivalent to the Kolmogorov–Smirnov distance between the empirical distribution function FN (x) of the...

Another measure of discrepancy for numeric sequences is the star discrepancy D∗ N , which is equivalent to the Kolmogorov–Smirnov distance between the empirical distribution function FN (x) of the sequence and the uniform distribution function F(x) = x on [0, 1]. Show that D∗ N ≤ DN ≤ 2D∗ N .