Let be a measure on the set of natural numbers.
And define for
My solution so far:
To be honest I'm a bit lost in this one. So should I have something like ?
Last edited by tttcomrader; Aug 26th 2011 at 08:09 AM.
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Originally Posted by tttcomrader Let be a measure on the set of natural numbers.
And define for Taking we get that :maybe there is a typo.
Sorry, n should be equal to 1, 2, 3, ... I changed it in the original post.
Ok. Hint: write the integral as (use monotone convergence theorem) and you are almost done. Compute the measure of for .
So would I have ?
Originally Posted by tttcomrader So would I have ? There shouldn't be any in the sum, since you sum over . We have .
Thanks! I understand how the measure will sum up now. But what would x become? Does it become n, n+1, ...?
We have , since on we must have .