## Abstract The measurable list chromatic number of a graph __G__ is the smallest number ΞΎ such that if each vertex __v__ of __G__ is assigned a set __L__(__v__) of measure ΞΎ in a fixed atomless measure space, then there exist sets $c(v)\subseteq L(v)$ such that each __c__(__v__) has measure one an
Measurable Sets With Excluded Distances
β Scribed by Boris Bukh
- Publisher
- Springer
- Year
- 2008
- Tongue
- English
- Weight
- 411 KB
- Volume
- 18
- Category
- Article
- ISSN
- 1016-443X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract In an ordinary list multicoloring of a graph, the vertices are βcoloredβ with subsets of preβassigned finite sets (called βlistsβ) in such a way that adjacent vertices are colored with disjoint sets. Here we consider the analog of such colorings in which the lists are measurable sets fr
## Abstract Let ΞΌ be a Radon measure with compact support in IR^n^ such that equation image We show that the imw of ΞΌ x ΞΌ under the distance map (x, y) β |xβ y| is an absolutely continuous measure with density of class C^a^β(n+1)/2. As a corollary we get that If AC IR^n^ is a Suslin set with Haus