# Measurable chromatic numbers

```@article{Miller2008MeasurableCN,
title={Measurable chromatic numbers},
author={Benjamin D. Miller},
journal={Journal of Symbolic Logic},
year={2008},
volume={73},
pages={1139 - 1157}
}```
• B. D. Miller
• Published 1 December 2008
• Mathematics
• Journal of Symbolic Logic
Abstract We show that if add(null) = c, then the globally Baire and universally measurable chromatic numbers of the graph of any Borel function on a Polish space are equal and at most three. In particular, this holds for the graph of the unilateral shift on [ℕ]ℕ, although its Borel chromatic number is ℵ0. We also show that if add(null) = c, then the universally measurable chromatic number of every treeing of a measure amenable equivalence relation is at most three. In particular, this holds for…
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