How would you prove that for

where is a sigma algebra of and is a counting measure.

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- May 9th 2010, 02:59 PMwilly0625counting measure space inclusion
How would you prove that for

where is a sigma algebra of and is a counting measure. - May 9th 2010, 04:17 PMJose27
- May 9th 2010, 04:53 PMmabruka
One question:

So you have for

What if some of the first N-1 terms of x are greater than 1, so that for some ? - May 9th 2010, 05:00 PMJose27
- May 9th 2010, 06:45 PMJose27
I think I have an answer so if anyone's interested here it goes:

Since the inclusion is clearly linear we only have to prove that it's continous at . Take such that as . There exists an such that if then so we must have for all and , but by the argument used to prove the inclusion we then have so that it is continous at .