Suppose that and in measure.

Then .

Proof so far.

Now, and .

So for the first case, then

But how does the lim inf turn into lim sup?

Thank you!

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- Nov 19th 2009, 08:40 AMtttcomraderLiminf to limsup
Suppose that and in measure.

Then .

Proof so far.

Now, and .

So for the first case, then

But how does the lim inf turn into lim sup?

Thank you! - Nov 19th 2009, 09:55 AMJose27
What does "in measure" mean? If i'ts pointwise convergence a.e. with respect to the measure couldn't you apply Fatou two times (to and ) to get that

As for your question - Nov 20th 2009, 10:49 AMMoo
Convergence in measure :