How to find an example for a measure which is not continuous from above?

measure-theory

Well, since $A_n = \mathbb{N} \setminus \{1,\dots , n\}$ has infinitely many elements for any $n$, we must have $$\mu(A_n) = \infty.$$ Now what can you conclude about $\lim_{n\rightarrow \infty} \mu(A_n)$?

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