Is there a formula for the Haar measure on a product of groups?

Question

Let $ (G_{n})_{n \in \mathbb{N}} $ be a sequence of locally compact topological groups with a corresponding sequence $ (\mu_{n})_{n \in \mathbb{N}} $ of Haar measures. Is there a way to construct a Haar measure on the product group $ \displaystyle \prod_{n \in \mathbb{N}} G_{n} $ using $ (\mu_{n})_{n \in \mathbb{N}} $? Is the task easier if the product is finite, or if all of the $ G_{n} $’s are compact?