2 problems

Let $n\ge 2$, let $\mathcal P^{n-1}=\{(\xi,|\xi|^2):\xi\in\mathbb R^{n-1}\}\subset\mathbb R^n$, and let $f$ satisfy…

Given an analytic family $\mathcal{F}$ of curves in $\mathbb{R}^{2}$, characterize when there exists a Borel set $E\subset\mathbb{R}^{2}$ with Lebesgue measure $|E|=0$ such that, f…