# Question regarding notation in integrals (measure theory)

The definition of a product measure is given as

$$(\mu_1\otimes\mu_2)(A) =\int_{\Omega_1} \mu_2(A_{\omega_1})\mu_1(d\omega_1)$$

This is the same as

$$(\mu_1\otimes\mu_2)(A) =\int_{\Omega_1} \mu_2(A_{\omega_1})d\mu_1$$

where $\omega_1 \in \Omega_1 \in \mathcal{A_1}$ with measure $\mu_1$.

Is this correct or does $\mu_1(d\omega_1)$ mean something else?