This question popped to my mind during an analysis lecture:
Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a (general) function. Is there an $N\subset \mathbb{R}^2$ with $\lambda^2(N)=0$, such that $\{(x,f(x)):x\in \mathbb{R}\}$ $\subset N$ ?
If $f$ is measurable or even continuous, we could apply classical calculus, but what if f is not measurable?
