Structural properties of extremal asymmetric colorings

• Veröffentlicht in: Algebra and Discrete Mathematics
• Datum: 2003
• 1. Verfasser: Verbitsky, O.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2003
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/155696
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Structural properties of extremal asymmetric colorings / O. Verbitsky // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 4. — С. 92–117. — Бібліогр.: 12 назв. — англ.

Let Ω be a space with probability measure µ for which the notion of symmetry is defined. Given A ⊆ Ω, let ms(A) denote the supremum of µ(B) over symmetric B ⊆ A. An r-coloring of Ω is a measurable map χ : Ω → {1, . . . , r} possibly undefined on a set of measure 0. Given an r-coloring χ, let ms(Ω; χ...