Erratum -- Brook's theorem for measurable colorings
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Proposition 2.1. of the paper is only true if we assume that the measure \mu or topology \tau is quasi-invariant, and is false in general.
There simply isn't a nice connection between measurable colorings and Borel colorings mod null in the non-quasi-invariant setting.
This error does not impact any the rest of the paper since elsewhere we always assume our measures/topologies are quasi-invariant as explanined in the discussion following Proposition 2.1.
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Throughout the paper, "König's lemma" should be replaced by "Kőnig's lemma".