All Questions

Say that a function $f(t)$ “changes only by jumps” if $f(t) + \text{const} = C ∑_k j_k θ(t-t_k)$ for a certain constant $C$. Here $θ(t)$ is the Heaviside step function which has a jump 1 at $t=0$ (it ...

Erdős' similarity conjecture states that for each infinite set $A\subset \mathbb R$ there is a set $P\subset [0,1]$ of positive measure such that for all $t\in \mathbb R$, $\delta\neq 0$ there is some ...

This question came up (unexpectedly) in a problem I was working on a few years ago. It may not be too difficult but I never got around to figuring out the answer, because all I needed at that time was ...