In set theory, it is important to work with the notion of a family or indexed collection of sets. In the theory of stochastic processes, for example, this concept is widely used, mainly for filtering theory in sigma-algebras. Indexed collection Definition (Indexed family of sets) Let $\Gamma$ be a set, we assume that for each element $\gamma \in \Gamma$ a set $A_{\gamma}.$ is associated. The collection of such sets $A_{\gamma}$ is said to be an indexed family of sets, indexed by the set $\Gamma$ and denoted by $$\\{A_{\gamma}; \gamma \in \Gamma \\}$$