What does the "$\bigwedge$" symbol mean in "$\bigwedge_{j=1,\ldots,M,j\neq i}\Delta_i(x)>\Delta_j(x)"$?

Question

What does the "$\bigwedge$" symbol mean in the following?

I assume it means "and". Am I right?

Answer 1

It is the conjunction of all predicates evaluated where the index is in the indicated domain.

EG: $\lower{1ex}{\left[\raise{1ex}{\bigwedge\limits_{j\in\{1,2,3\}} P_j}\right]} ~=~ P_1\wedge P_2\wedge P_3$

So we are taking the measure for the probability of the event where $\Delta_i(\chi)$ is greater than $\Delta_j(\chi)$ for all $j$ in the integer domain $\{1..M\}$ except when $j=i$.

$$\Pr\left\{\raise{1.25ex}{\mathop{\bigwedge\qquad\quad}_{j\in\{1..M\}: j\neq i}\hspace{-6ex}\bigl[\Delta_i(\chi)>\Delta_j(\chi)\bigr]}\right\} $$

Answer 2

It is the conjunction, like $P \wedge Q$, of all the things. Here $j$ ranges over $1$ to $M$ except for $i$. This will be true when $\Delta_i(x)$ is greater than all the rest.