✦ LIBER ✦
Translations of nets and relationship between supreme andLκ-discrepancies
✍ Scribed by Vsevolod F. Lev
- Book ID
- 104625597
- Publisher
- Akadmiai Kiad
- Year
- 1996
- Tongue
- English
- Weight
- 364 KB
- Volume
- 70
- Category
- Article
- ISSN
- 1588-2632
No coin nor oath required. For personal study only.
✦ Synopsis
As it is shown in [1], L2-discrepancy may substantially (by the order of value) vary under translates of net modulo the unit cube Q~. We prove here, that for all ~ > 1 the supremum of L~-discrepancies of all such translated nets coincides (up to a multiplicative constant) with the supreme discrepancy:
sup D~(S + ~) × D~(S).
c~EQ ~"
1. Notation
We use the notation of [1]. Vectors in R s are denoted by small latin or Greek letters, as x(k),a, and so on. Lower indices are reserved for vector coordinates, as x~k);c~s. The following two vectors are written in bold to distinguish from scalars: 0 --(0,...,0