Suppose in measure, and in measure, prove that (a) in measure and that (b) in measure if , not if
Proof so far.
(a) I think this is pretty easy.
I know that , we have and .
Question 1: Is this really right? I took this from a proof in the book, but I'm failing to fully understand why it is true.
So it follows that
Therefore proved (a). Is this right?
For (b), I know that I need to show that:
But umm... a bit stuck here, how should I incorporate the fact that ?