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](https://en.wikipedia.org/wiki/Irrational_rotation). 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?



Who first proved ergodicity of irrational rotations of the circle?
the proof goes back to [Nicole Oresme](https://en.wikipedia.org/wiki/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


* [Nicole Oresme and the commensurability or incommensurability of celestial motions](https://www.jstor.org/stable/41133220) *(contains an annotated English translation of Oresme's Latin text)*
* [Oresme's Proof of the Density of Rotations of a Circle through an
Irrational Angle](http://ac.els-cdn.com/S0315086083710347/1-s2.0-S0315086083710347-main.pdf?_tid=393a75fe-3a09-11e7-88d7-00000aab0f02&acdnat=1494919874_03f2e08c5326fde1e60c0c41b4f78974)
* [Nicole Oresme and the ergodicity of rotations](https://www.cambridge.org/core/books/creating-modern-probability/supplement-nicole-oresme-and-the-ergodicity-of-rotations/888A10AE26F82DF13E839C221B1B93F3)


