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?
Best Answer
the proof goes back to Nicole Oresme in his paper De commensurabilitate vel incommensurabilitate motuum celi [On the Commensurability or Incommensurability of the Motions of the Heavens], dated around 1360, see