Let us consider a symplectic manifold $(M,\omega)$. By means of this structure, I can easily define a symplectic measure $\mu(M)$ on $M$ by considering the "right number" of wedge product of the symplectic $2$-form.
By means of a non-holonomic constraint $F=0$ and an embedding map $i$, I can define a presymplectic sub-manifold $\Sigma$ of $M$, whose presymplectic form is defined by the pull-back of $\omega$ to $\Sigma$ as $\omega_\Sigma=i^*\omega$.
Maybe this is a silly question, but I am wondering if the pull-back of the symplectic measure $\mu(M)$ on $M$ defines a measure $\mu(\Sigma)$ on $\Sigma$. And, if this is the case, has it a relation with the presymplectic form on $\Sigma$? Does the degeneracy of the latter play a role in the definition of the measure?
Thank you very much for your attention!