All Questions

Problem. Is there a partition $\mathbb R^2=A\sqcup B$ of the Euclidean plane into two Lebesgue measurable sets such that for any disk $D$ of the unit radius we get $\lambda(A\cap D)=\lambda(B\cap D)=\...

I have a question regarding sets of finite perimeter. In particular I'm interested to find $$\mu_{E \cap H_t}, \label{1}\tag{1}$$ where $E$ is a set of finite perimeter in a generic open set $\Omega \...

In this post it was shown that if $\Omega$ and $\Omega'$ are diffeomorphic non-empty open domains in some Euclidean space then the corresponding local Sobolev spaces are diffeomorphic with ...

I am looking for a version of Lebesgue density theorem that works when restricting to "good" collections of balls with respect to (not necessarily doubling) metric measure spaces. Specifically Let $(...