False equivalence. My heart sinks, as does yours, at the mere sight of these words. But just when I was ready to post a picture of a great new beer -- from Utah! -- plus some interesting/alarming ...
Let $(X, \mathscr{B})$ be a standard Borel space, $R \subset X \times X$ an equivalence relation $\in \mathscr{B} \times \mathscr{B}$. Assume each equivalence class ...