Discrepancy

We consider some informal definitions or characteristics of discrepancy in this section. Later we give the formal mathematical definition.

Definition 1 (Discrepancy)   Discrepancy is a measure of the departure from the uniform covering of a set of numbers in a box in n-dimensional space.

There are several different measures of discrepancy. The most important is called the "Star Discrepancy". A set of N points uniformly spaced from 0 to 1 on the line have a Star Discrepancy of $\frac{1}{2N}$. This goes to 0 as N goes to infinity. This set of points is a uniform finite covering of the interval 0 to 1. As N goes to infinity, it becomes, for certain integration purposes, a uniform covering of the interval and its Star Discrepancy goes to zero.