Measurable versions of the Lovász Local Lemma and measurable graph colorings

@article{Bernshteyn2019MeasurableVO,
  title={Measurable versions of the Lov{\'a}sz Local Lemma and measurable graph colorings},
  author={Anton Bernshteyn},
  journal={Advances in Mathematics},
  year={2019}
}
In this paper we investigate the extent to which the Lov\'asz Local Lemma (an important tool in probabilistic combinatorics) can be adapted for the measurable setting. In most applications, the Lov\'asz Local Lemma is used to produce a function $f \colon X \to Y$ with certain properties, where $X$ is some underlying combinatorial structure and $Y$ is a (usually finite) set. Can this function $f$ be chosen to be Borel or $\mu$-measurable for some probability Borel measure $\mu$ on $X$ (assuming… Expand

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