- #1
LHeiner
- 8
- 0
Hey
i'm given a measure on [tex]$\Omega =\mathbb{N}, A \subset \mathbb{N}$[/tex] and should check additivity as well as [tex]$\sigma$[/tex]-additiviy. Additionally i should give an example for a set where [tex]$\mu(A)$[/tex] is not defined:
[tex]$\mu(A)=\lim_{n \rightarrow \infty} \frac{1}{n} \xi\mid _\mathbb{N} (A \cap [1,n])$[/tex] with finite limit.
whereas [tex]$\xi\mid _\mathbb{N}$[/tex] is the counting measure on [tex]$\mathbb{N}$[/tex]
Can anybody help me with this?
Appreciate it, thanks very much
i'm given a measure on [tex]$\Omega =\mathbb{N}, A \subset \mathbb{N}$[/tex] and should check additivity as well as [tex]$\sigma$[/tex]-additiviy. Additionally i should give an example for a set where [tex]$\mu(A)$[/tex] is not defined:
[tex]$\mu(A)=\lim_{n \rightarrow \infty} \frac{1}{n} \xi\mid _\mathbb{N} (A \cap [1,n])$[/tex] with finite limit.
whereas [tex]$\xi\mid _\mathbb{N}$[/tex] is the counting measure on [tex]$\mathbb{N}$[/tex]
Can anybody help me with this?
Appreciate it, thanks very much