Let $n\in\mathbb{N}$, let $U\subseteq \mathbb{R}^n$ be \reftext{def:open-subset-euclidean-space-2026a}{open}, let $k\in\mathbb{N}\cup\{0\}$, and let $\omega$ be a \reftext{def:differential-k-form-euclidean-open-set-2026a}{differential $k$-form} on $U$. Then there exist unique real-valued functions

indexed by strictly increasing $k$-tuples $(i_1,\dots,i_k)$ with $1\le i_1<\cdots<i_k\le n$ such that

where each $dx_i$ is the coordinate $1$-form from \ref{def:coordinate-1-form-euclidean-open-set-2026a} and the wedge product is the one from \ref{def:wedge-product-differential-forms-euclidean-2026b}. When $k=0$, this says that $\omega$ is uniquely equal to a real-valued function on $U$.