What does $e^{\mu}$ mean for a measure $\mu$?

Question

I have seen the notation $\int_M fe^{\mu}$ in some geometry books and I cannot even guess what $e^{\mu}$ might mean for a measure/form $\mu$ on the (symplectic) manifold $M$.

Any clarifications are appreciated.

Edit

Answer 1

If $e^{\mu}=d\lambda$ for some measure $\lambda$ in $M$ then, it seems that $\mu=\ln(d\lambda)$. But here is not clear whether $\ln(d\lambda)$ is a measure.

Answer 2

I found this remark in a book by Guillemin, Ginzburg, and Karshon:

It is convenient to work with the differential form (of mixed degree) $$\exp \omega=1+\omega+\frac{1}{2!}\omega\wedge\omega\dots .$$ With the convention that $\int_M\beta=0$ if the degree of $\beta$ is different than the dimension of $M$, Liouville measure is given by integration of $\exp \omega$.

This shows that my guess in the above comments was correct! However, I would appreciate if an expert would clarify why it is "convenient" to work with this differential form of mixed degrees.