Writing notation for pushforward measures

Question

I have the following notation, $\gamma=(\operatorname{id},T)_{\#}\mu$, where $\mu$ is a probability measure on $X$, $\gamma$ on $X \times Y$ and $T$ a function from $X$ to $Y$. I get that the $_{\#}$ indicates a pushforward measure, but I don't know how to interpret the fact that this pushforward is through both $T$ and $\operatorname{id}$.

Answer 1

This notation refers to the measure $ \gamma = \text{id}_{\#}\mu \times T_\#\mu = \mu \times T_\#\mu. $