Exercise 4, § 3

Let T be the interval [0, 1] of $\mathbf{R}$, $\mu$ the Lebesgue measure on T. Let R$\{x, y\}$ be the equivalence relation $x - y \in \mathbf{Q}$ in T. Show that R is not $\mu$-measurable (apply Th. 3 of No. 4), but the graph of R in $T \times T$ is negligible for the product measure $\mu \otimes \mu$.