A note on measure-theoretic domatic partitions

Abstract

We show that if $(X,\hat{I}¼)$ is a standard probability space, then every $\hat{I}¼$-preserving ${\aleph }_0$-regular Borel graph on $X$ admits a $\hat{I}¼$-measurable vertex ${\aleph }_0$-coloring in which every vertex sees every color in its neighborhood.

Superseded by the newer version of arXiv:2205.05751