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 .

Now, since

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 ?

Thank you!