Timeline for Example of measure for some algebra over N
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 5, 2018 at 11:08 | comment | added | YCor | Why don't you correct, amend or delete your post, since it's been mentioned that it's wrong? | |
| Dec 4, 2018 at 17:16 | comment | added | Robert Furber | For the record, $\mu$ is not finitely additive. We can build a subset $A$ of $\mathbb{N}$ such that the limsup is strictly larger than the liminf. Then, because $1-x$ is an order-reversing isomorphism of $[0,1]$, $$\mu(\mathbb{N}\setminus A) = 1 - \limsup_{n \to \infty} \frac{|A \cap \{1,\ldots,n\}|}{n} < 1 - \mu(A)$$. | |
| Dec 3, 2018 at 9:36 | comment | added | Dirk | Your algebra $\mathcal{A}$ is $\mathcal{P}(\mathbb{N})$, right? But this is already a $\sigma$-algebra, so the extension of $\mu$ is $\mu$ itself which is not countable additive, or do I miss something? | |
| Dec 3, 2018 at 9:24 | history | answered | Dominic van der Zypen | CC BY-SA 4.0 |