If is an outer measure on X and is a sequence of disjointed measurable sets, prove that
Proof so far.
Since is an outer measure on , we know that:
And since is -measurable, then for each n, we have
Now, since is an outer measure.
So what is left to prove is that
So I have
And I know I will have to use the measurable property, but I don't seem to be making any progress here...
Any hints? Thank you.