Erratum -- Brook's theorem for measurable colorings

• 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.
• Throughout the paper, "König's lemma" should be replaced by "Kőnig's lemma".
• On page 12, line -11, $G \restriction (A \setminus [\bigcup_n A_n]_{E_G})$ should be $G \restriction (X \setminus [\bigcup_n A_n]_{E_G})$. (I.e. the A should be replaced by X)

Thanks to Katalin Berlow for pointing out the last two typos.