A simple proof of reflexivity and separability of $N^{1,p}$ Sobolev spaces

Ryan Alvarado, Piotr Hajłasz, Lukáš Malý

We present an elementary proof of a well-known theorem of Cheeger which states that if a metric-measure space $X$ supports a $p$-Poincaré inequality, then the $N^{1,p}(X)$ Sobolev…