I'm learning about differential forms and orientation. I encountered the following theorem:
Let $M$ be an oriented Riemannian manifold. There exists a unique volume form $\omega$ such that for all $p\in M$ and every orthonormal, positively-oriented ordered basis $\{b_1,\dots, b_n\}$ of $T_pM$, $\omega_p(b_1,...,b_n)=1$.
I wasn't able to find any proof online or in Lee's book and I'm not sure how to approach this. Any help would be appreciated.