show/hide this revision's text 2 added parenthetical comments

The short answer (to the question in the title) is so that you don't need to worry about whether E is measurable. If you happen to know that E is measurable then you can drop "outer" everywhere.

There may be a longer answer (better addressing the question as stated in the page) involving specific applications where E is in fact nonmeasurable, but I personally don't know of such applications offhand.

show/hide this revision's text 1

The short answer is so that you don't need to worry about whether E is measurable. If you happen to know that E is measurable then you can drop "outer" everywhere.

There may be a longer answer involving specific applications where E is in fact nonmeasurable, but I personally don't know of such applications offhand.