While I was reading Durrett "Probability Theory and Examples" I found some problem in the notation of the following part:
"To formulate the third and final condition for $F$ to define a measure, let $$A=(a_1,b_1]\times (a_2,b_2] \times \dots \times (a_d,b_d] $$ $$V=\{ a_1,b_1\} \times \{ a_2,b_2\} \times \dots \times \{ a_d,b_d\} $$ where $-\infty <a_i<b_i<\infty$. To emphasize that $\infty$ are not allowed, we will call $A$ a finite rectangle. Then $V$=the vertices of the rectangle $A$. If $v\in V$ , let $$sgn(v) =(-1)^{\# of\space a's\space in\space v}$$ $$\Delta_A =\sum_{v\in V} sgn(v) F(v)$$"
Here the context is about the extra conditions of $F$(distribution function) to extend in $d$ dimension. The problem is $A$ is product of intervals, so it is interval but $V$ contains the product of the set of start points and end points, in a way it makes sense that the vertices are $\{ (a_1, a_2, \dot , a_d), (a_1, b_2, \dot , a_d),\dots$etc. Then what does "# of $a$'s in $v$" means?
May be it is a silly doubt but I would be thankful for any help.