Star Discrepancy

Given a point set  in the -dimensional unit cube , the star discrepancy is defined as

(1)

where the local discrepancy is defined as

(2)

 is the content of , and  is the class of all -dimensional subintervals  of  of the form

(3)

with  for . Here, the term "star" refers to the fact that the -dimensional subintervals have a vertex at the origin.

REFERENCES:

Entacher, K. "Discrepancy Estimates Based on Haar Functions." Math. Computers in Simulation 55, 49-57, 2001.