Abstract
Let $\Gamma$ be a countable group and let $G$ be the Schreier graph of the free part of the Bernoulli shift of $\Gamma$. We show that the Borel fractional chromatic number of $G$ is equal to $1$ over the measurable independence number of $G$. As a consequence, we asymptotically determine the Borel fractional chromatic number of $G$ when $\Gamma$ is the free group, answering a question of Meehan.
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