TITLE: Who first proved ergodicity of irrational rotations of the circle?
QUESTION [26 upvotes]: It is a classic result that the irrational rotations of the circle are ergodic. Formally, let $T:\mathbb{T}\to \mathbb{T}$ be defined by $Tz=ze^{2\pi i\alpha}$. If $\alpha$ is irrational, then $T$ is ergodic. This result appears in many textbooks (e.g., Walters, An Introduction to Ergodic Theory), and even in Wikipedia. However, none of these refer to the original. A Google Scholar search didn't help either.
My question is simply, who was the first to prove or to notice this result, and is there a reference to the original paper?

REPLY [2 votes]: Weyl had only one "big" paper on uniform distribution theory, which is the 1916 paper. However, the fact that $(n \alpha)$ is equidistributed for irrational $\alpha$ is usually attributed to Bohl, Spierpinski and Weyl (independently), who proved it in 1909-1910. However, they did not prove anything about ergodicity. The ergodicity question does not ad-hoc have any close relation to the equidistribution problem.