Let $A\subset\mathbb{N}$ and $2A=A+A=\{a+b \lvert a,b\in A\}$ and $3A=2A+A$. I wonder how small the density of $3A$ can be, knowing that the density of $2A$ is, say, $\beta >0$, but not knowing anything about $A$ (assuming all three have densities).

I would be equally interested in the similar question for measurable sets in the circle $\mathbb{R}/\mathbb{Z}$, or finite sets of $\mathbb{Z}/p\mathbb{Z}$.

Thanks !


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.