It the previous question of mine I put a reference which shows that any $\omega$-regular language over the alphabet $\Sigma$ is a Borel subset of $\Sigma^\omega$. I am not sure whether the reference I am aware of is the first the showed this result, so I wonder whether there are other papers the contain it. Alternatively, I am also interested in textbooks that contain the proof of this fact.

It the previous question of mine I put a reference which shows that any $\omega$-regular language over the alphabet $\Sigma$ is a Borel subset of $\Sigma^\omega$. I am not sure whether the reference I am aware of is the first the showed this result, so I wonder whether there are other papers the contain it. Alternatively, I am also interested in textbooks that contain the proof of this fact.