How I can show that every finite measure can be regarded as a $\sigma$-finite measure but not conversely in general?
Finite measures are $\sigma$-finite
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measure-theory
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6Please write down definition if sigma-finitness. Think of usage of empty sets – 2012-05-13
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3For the converse, consider Lebesgue measure on $\Bbb R$. – 2012-05-13