Dears;

Could you help me to prove the measure space(in the attachment) hold the countably additive?

Attachment 23886

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- May 16th 2012, 02:12 PMraedCountably additive for special set
Dears;

Could you help me to prove the measure space(in the attachment) hold the countably additive?

Attachment 23886 - May 16th 2012, 02:13 PMraedRe: Countably additive for special set
Best Regards

- May 16th 2012, 02:15 PMraedRe: Countably additive for special set
and the countably additive

Attachment 23887 - May 16th 2012, 03:13 PMemakarovRe: Countably additive for special set
There exist two disjoint sets with countable complements...

- May 17th 2012, 03:50 AMraedRe: Countably additive for special set
- May 17th 2012, 07:33 AMemakarovRe: Countably additive for special set
You can take $\displaystyle E_1 $ and $\displaystyle E_2 $ to be two disjoint sets with countable complements and $\displaystyle E_i=\emptyset $ for i > 2. Then the left-hand side of the definition of countably additive measure is 1 while the right-hand side is 2.

- May 17th 2012, 08:19 AMraedRe: Countably additive for special set
- May 17th 2012, 08:21 AMemakarovRe: Countably additive for special set
I think this function is not a measure because it is not additive.