in . Show that in measure.

any hint would be appreciated.

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- Dec 31st 2009, 12:24 PMArchiconvergence in measure
in . Show that in measure.

any hint would be appreciated. - Dec 31st 2009, 12:36 PMMoo
Hello,

and since the LHS goes to 0 (convergence in Lē), then the RHS goes to 0 too, and hence the convergence in measure. - Dec 31st 2009, 02:10 PMArchi
- Jan 2nd 2010, 12:11 AMMoo
I'm rephrasing it (Doh)

Since converges to in Lē, then by definition of the convergence in Lē, the red part goes to 0 as**n goes to infinity**

Thus by the sandwich theorem, the blue part goes to 0 as n goes to infinity.

When it is said "for all epsilon", it's like you choose any epsilon and you**fix**it. So it's like a constant !

Thus , which means, by definition, that converges to in measure.

Looks better ? - Jan 2nd 2010, 12:44 AMArchi