Probability distribution on trajectories of stochastic process. In Nelson's book "Radically Elementary Probability Theory", chapter 3, he defines a stochastic process over a finite probability space $\left<\Omega,pr\right>$ and indexed by a finite set $T$ as a function $\psi : T \rightarrow \mathbb{R}^{\Omega}$.  (Hence $\psi (t)(\omega) \in \mathbb{R}$ for any $t\in T$ and $\omega \in \Omega$.)  Then he goes on to define a trajectory of the stochastic process as $\psi(\cdot)(\omega)$ for any $\omega \in \Omega$.  
Next he defines $\Lambda_{\psi}$ to be the set of trajectories of $\psi$, and he defines a probability distribution $pr_{\psi}$ by $$pr_{\psi}(\lambda) = Pr\left\{\psi(t) = \lambda(t) \: \forall t \in T\right\}$$
He claims that $\left<\Lambda_{\psi},pr_{\psi}\right>$ is then a finite probability space. 
Question: The author is using some probabilistic shorthand in his definition of $pr_{\psi}$, which is totally opaque to me.  Can someone please spell out more explicitly what is the proper definition of $pr_{\psi}$? 
Bonus points if you can illustrate with with an example--e.g. $\Omega = \{H,T\}$ as a model of a coin flip. 
 A: Earlier, the author defined for a subset $A\subset\Omega$,
$$Pr(A):=\sum_{\omega\in A}pr(\omega).$$
Very often in probability, if $X$ is a random variable defined on $\Omega$, we will use the abbreviation $\{X\in A\}$ for the set $\{\omega\in\Omega:X(\omega)\in A\}$. So the full definition of $pr_\psi$ is
$$pr_\psi(\lambda):=Pr\{\omega\in\Omega:\psi(t)(\omega)=\lambda(t)\text{ for all }t\in T\}=\sum_\omega pr(\omega)$$
where the sum is over all $\omega\in\Omega$ such that $\psi(t)(\omega)=\lambda(t)$ for all $t\in T$. To see that $(\Lambda_\psi,pr_\psi)$ is a finite probability space, notice that $\Lambda_\psi$ is simply the range of the function $\Omega\to\mathbb R^T:\omega\mapsto\psi(\cdot)(t)$ which must be finite since $\Omega$ is finite. Now if we sum over $\lambda\in\Lambda_{\psi}$, we find
$$\sum_{\lambda\in\Lambda_{\psi}}pr_\psi(\lambda)=\sum_{\lambda\in\Lambda_\psi}\sum_{\omega:\psi(\cdot)(\omega)=\lambda}pr(\omega)=1$$
since each $\omega\in\Omega$ appears in the double sum exactly once.
For an example, let's consider tossing a coin $3$ times. Our probability space is
$$\Omega:=\{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\},\\
pr(\omega):=\frac18\text{ for all }\omega\in\Omega.$$
A random variable on this space could be the total number of heads, or $5$ if the first toss is a tail and $1$ otherwise, or the number of tails in the first two tosses minus the number of heads in the third toss, etc. A stochastic process with index set $T=\{1,2,3\}$, on the other hand, would be something like
$$\psi(t):=\{\text{the number of heads after the first $t$ throws}\}.$$
In this case, our space of trajectories is
$$\Lambda_\psi=\{(1,2,3),(1,2,2),(1,1,2),(1,1,1),(0,1,2),(0,1,0),(0,0,1),(0,0,0)\}$$
and our probability distribution is
$$pr_\psi(\lambda)=\frac18\text{ for all }\lambda\in\Lambda_\psi.$$
One can imagine, without too much difficulty, that if you chose a more complicated definition for $\psi$, we could have multiple values of $\omega$ yield the same trajectory, in which case we would get a different $pr_\psi$.
For what it's worth, I find this a rather strange way to teach probability and stochastic processes.
