Unclear about the meaning of the question

Question

I am reading Probability and Stochastics by Erhan Cinlar. I came across a question which I do not understand part of it. This is the question:

A function $f$ on $E$ is said to be elemenentary if it has the form $f=\sum\limits^{\infty}_{1}a_i1_{A_i}$ where $a_i\in\bar{\mathbb{R}}$ and $A_i\in\mathscr{E}$ $\underline{\text{for each }i\text{, the }A_i\text{ being disjoint}}$. Show that every such function is $\mathscr{E}$-measurable.

I do not understand the underline part of the above question. Does he mean pair-wise disjoint, i.e $\forall i\neq j, A_i\cap A_j=\phi$? Does he mean $\bigcap\limits_{i}A_i=\phi$? Or some other intersection between?

Thanks for your help

Answer 1

It means that are pairwise disjoint, i.e. $A_i\cap A_j=\emptyset$ if $i\neq j$.