**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.