Express a count of an element in period of time

Question

I want to know if it is possible to represent the count of an element in a set, having different elements collected over a given period of time.

Let's say $A$ is the set with varying elements at a given period of time. and $e$ is the element that I want to count.

Basically, I want to say something like this in an equation. $E_{count}=count(e, A)$

Any help

Answer 1

One possibility is to introduce an index that encode the set of period of time, $A_T$.

Suppose $T=\bigcup T_i$ is a partition of the time interval,

$$count(e,T)=count\left(e,\bigcup_iT_i\right)=\sum_icount\left(e,T_i\right)$$