The following definition is from this paper in page 72.
$\textit{Definition:}$ A communication mechanism is a triple $\mathfrak{C}=((T_i)_i, (Y_i)_i , l )$, where $T_i$ is $i's$ finite set of messages, $Y_i$ is $i's$ finite set of signals, and $l: T\to \Delta(Y)$ is the signal function. When $t$ is the profile of messages sent by the players, $y\in Y$ is drawn according to $l(t)$ and player $i$ is informed of $y_i$. $\mathfrak{T}_i=\Delta(T_i)$ represents the set of mixed messages for player $i$ and $l$ is extended to $\mathfrak{T}$ by $l(\tau)( y)=\mathbb{E}_{\tau} l(t)( y)$.
$\textit{Question 1:}$ What is this $\tau$ probability measure and why is this defined in this way, namely what is the intuition behind this? Apparently, the way that the communication mechanism is defined comes from the measure theory, but how did he end up with the $l$ function defined under a $\tau$ probability measure?
$\textit{Question 2:}$ What is the meaning of $l(t)(y)$, does this mean $l(t,y)$? I have never seen this symbolism $l(t)(y)$ again.
Thank you in advance!