How is a communication protocol a mechanism? Given a finite set $\Sigma$ and a positive integer $n$, a mechanism is a set $\{ \mu_x \vert x \in \Sigma^n \}$ such that $\mu_x$ is a probability measure on some $\sigma-$algebra for each $x$. 

Now given a communication protocol $P$ between two privately coin-flipping parties $A$ and $B$ who start with the inputs $x$ and $y$ respectively one defines this quantity called the $VIEW^A_P(x,y)$ : ``a joint probability distribution over $x$, the transcript of the protocol $P$, private randomness of the party $A$, where the probability space is private randomness of both parties" 


What does the stuff in the quotes mean? 
Can someone help understand how is this $VIEW^A_P(x,y)$ a ``mechanism" as defined earlier? (For this to be a mechanism, $VIEW^A_P(x,y)$ for a fixed $x$, has to assign a probability to some set of outcomes and I am unable to see as to which set of outcomes is it assigning a probability and how) 




A transcript of a protocol will be a sequence of private coin tosses and bits exchanged in every step. So if one fixes both $x$ and $y$ then I can imagine that a probability can be assigned to a protocol - which would be the probability for that sequences of coin tosses to have happened. But still whaht is an "event" here is not clear since I can't see a natural way to group together these "outcomes" (each of which is now a possible transcript when started with a $x$ and $y$). 

But if one fixes only $x$ then nothing is clear to me..



Reference : http://www.cs.toronto.edu/~toni/Courses/CommComplexity2/Lectures/diffprivacy.pdf
The view of Alice is what Alice gets to see; it is a probability distribution that depends on the inputs of both players $x,y$. It is a distribution over triples $(x,\tau,r_A)$, where $x$ is Alice's input, $\tau$ is the transcript of the protocol, and $r_A$ is Alice's private randomness. This probability distribution depends both on $x$ and on Bob's input $y$.

Here is how to generate this probability distribution, given a protocol $P$ and the inputs $x,y$ of both players. Generate the shared randomness $r$ according to its distribution, and Alice's private randomness $r_A$ according to its distribution. Run $P$, obtaining a transcript $\tau$. Output $(x,\tau,r_A)$.