In a probability theory script, I read a definition of independence where I don't understand one detail (Let $(\Omega, \mathcal{F}, \mathbb{P})$ be a probability space)
"A family of events $(A_i)_{i \in I}$, $A_i \in \mathcal{F}$ is called independent if $\{A_i, \Omega\}$ [*] with $i\in I$ is independent." (def. 7.2.1c)
Just before there is definied: "Subsets $\mathcal{E}_i$, $i \in I$ of $\mathcal{F}$ are called independent if all finite combinations of them are independent." (which comes down to the usual formula $\mathbb{P}(A \cap B) = \mathbb{P}(A) \mathbb{P}(B)$)
Why do I have to introduce the $\Omega$ in [*] ?
(The source is this script: http://www.wias-berlin.de/people/koenig/www/WTSkript.pdf)