1997/10/01 by József Beck, J. Beck, William Chen +1
Mathematics · #Mathematical Approximation and Integration #Analytic Number Theory Research #Numerical methods in inverse problems
paper · doi:10.1112/s0024610797005267
Suppose that P is a distribution of N points in the unit square U=[0, 1]2. For every x=(x1, x2)∈U, let B(x)=[0, x1]×[0, x2] denote the aligned rectangle containing all points y=(y1, y2)∈U satisfying 0⩽y1⩽x1 and 0⩽y2⩽x2. Denote by Z[P; B(x)] the number of points of P that lie in B(x), and consider the discrepancy function D[P; B(x)]=Z[P; B(x)]−Nμ(B(x)), where μ denotes the usual area measure.