Geometric discrepancy revisited

Discrepancy theory addresses the general issue of approximating one measure by another one. Originally an offshoot of diophantine approximation theory, the area has expanded into applied mathematics, and now, computer science. Besides providing the theoretical foundation for sampling, it holds some of the keys to understanding the computational power of randomization. A few applications of discrepancy theory are listed. We give elementary algorithms for estimating the discrepancy between various measures arising in practice. We also present a general technique for proving discrepancy lower bounds