An inequality on the mass of image of rectifiable chain under chain map

Abstract

For a complete normed abelian group $G$, we show that the mass of image of a rectifiable $G$-chain $S$ under chain map $f_{\sharp}$ induced by Lipschitz map $f$ is controlled by the integral of Jacobi of $f$ restricted on the support of $S$ with respect to associated radon mesure $\mu_S$.