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Is counting measure indeed a measure and is this always sigma-finite?

Updated: 8/17/2019
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Jhhinuk17

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12y ago

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It is a measure, but it isn't always sigma-finite. Take your space X = [0,1], and u = counting measure

if u(E) < infinity, then E is a finite set, but there is no way to cover the uncountable set [0,1] by a countable collection of finite sets.

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12y ago
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Q: Is counting measure indeed a measure and is this always sigma-finite?
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