Let $n\in$ \reftext{def:natural-numbers-2026a}{$\mathbb{N}$}, let $\Omega,\Omega'$ be admissible domains in \reftext{def:euclidean-space-rn-2026a}{Euclidean space} $\mathbb{R}^n$ in the sense of \ref{def:continuous-n-form-support-euclidean-domain-2026a}, and let $F:\Omega\to\Omega'$ be an orientation-preserving \reftext{def:smooth-diffeomorphism-euclidean-half-space-domain-2026a}{smooth diffeomorphism}. Let $\omega$ be a continuous differential $n$-form on $\Omega'$ that is compactly supported in $\Omega'$, in the sense of \ref{def:continuous-n-form-support-euclidean-domain-2026a}.

Then the \reftext{def:smooth-diffeomorphism-euclidean-half-space-domain-2026a}{pullback} $F^{*}\omega$ is a continuous differential $n$-form on $\Omega$ that is compactly supported in $\Omega$, and

where both sides are integrals in the sense of \ref{def:integral-compactly-supported-n-form-euclidean-2026a}.