# Tagged Questions

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### Length of intersection of intervals

Can anyone prove this statement? It seems true, but I'm finding it tricky to give a concise proof.
Fix $\alpha\in[0,1]$. Let $\mu$ be Lebesgue measure. Define $B(c,r)\equiv[c-r,c+r]$, where $[\cdot, ...

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### Special functions on the unit disk

Let $\mathbb{D} = \{ (x,y) \in \mathbb{R}^2 \mid x^2 + y^2 < 1 \}$ be the unit disk.
We say a function $f : \mathbb{D} \rightarrow \mathbb{D}$ is a winner if it satisfies the following:
1) it is a ...