 Disjoint observation windows

Observation windows are measurable sets used to count points of a point process. They are pairwise disjoint when $W_i\cap W_j=\varnothing$ for every $i\ne j$. Half-open intervals such as $[0,1)$ and $[1,2)$ meet at a boundary without sharing any point, whereas the closed intervals $[0,1]$ and $[1,2]$ both contain one. A disjoint union makes window counts additive; it does not make their random variables independent.