In the following proof, why does the fact that imply that ?

http://www.math.purdue.edu/pow/sprin.../solution9.pdf

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- May 22nd 2010, 10:20 AMRandom Variablelimit proof
In the following proof, why does the fact that imply that ?

http://www.math.purdue.edu/pow/sprin.../solution9.pdf - May 22nd 2010, 11:06 AMmabruka
One way of seeing it:

Absolute value is a continuous function so

Where it was used the fact that since when then as well, we have

Finally

- May 22nd 2010, 11:08 AMmabruka
- May 22nd 2010, 11:25 AMmabruka
Certainly i dont understand how that step is done,

in fact it would seem to me that doesnt make any sense since the left side does not depend on x.

Returning to the proof, earlier we had that

for all n if

Taking and using the continuity of the abs value we get that since if then ,

in our case :

if then .

And we end up having from where the proof follows quite easily. - May 22nd 2010, 11:30 AMRandom Variable
- May 22nd 2010, 12:08 PMmabruka
Either a typo or some argument (which is not clear, at least for me) equivalent to the n-limit one. So far i dont see any flaws on this one.

- May 23rd 2010, 02:39 AMHallsofIvy