Let $(\mathbb R,Μ, \lambda)$ be the complete measure space of Lebesgue measurable subsets of $\mathbb R$, which has been constructed with the extension theorem. I got to show that the Product Measure in $(\mathbb R ^2$, $M⊗M$, $λ⊗λ$) is not complete by describing a set M ⊂ $\mathbb R ^2$ of which the Lebesgue measure is zero, meaning that for every ε > 0 there are finite-measure cuboids $Q_1$, $Q_2$,.. with M ⊂ $\cup_{n= 1}^\infty Q_n$ and $ \sum _{n=1}^{\infty} 1(λ ⊗ λ)(Q_n) < ε $ that aren't $λ ⊗ λ$-measurable.
I've got no idea how to work with these cuboids.