Über die isotrope Diskrepanz von Folgen. (On the isotropic discrepancy of sequences)
The isotropic discrepancy of a finite sequence \(w:=x_ 1,x_ 2,...,x_ N\) in the s-dimensional unit cube \(I^ s\) is defined by \(\sup_{C}| (A_ N(C)/N)-\lambda (C)|\) where the supremum is taken over all convex subsets C of \(I^ s\), \(A_ N(C)\) denotes the number of \(x_ i\) with \(x_ i\in C\) and \(\lambda\) is the s-dimensional Lebesgue measure. A method for estimating the isotropic discrepancy of a sequence directly is given, and is used for improving the known estimates for some of the most important sequences, as for example: The Hammersley sequence, the s- dimensional Halton sequence, the rotation on the s-dimensional torus.
scientific article; zbMATH DE number 3906593