Suppose we have the $(W_t)$ Brownian Motion and the filtration $F=(\mathcal{F}_t)$, where $\mathcal{F}_t:=\sigma(W_s;s\le t)$. I know that for any $n\in \mathbb{N}$ and $0\le t_0
They say: By the independence of $W_{t_i}-W_{t_{i-1}}$, $W_{t+h}-W_t$ is independent of the family of all increments $W_l-W_m$ with $m\le l\le t$, since it gives the independence for each finite subfamily.
I guess the last sentence means, that I can split $l-m$ into a finite "partition", like this: $l=t_0
It would be appreciated if someone could explain in a more detailed way, how we get this independence. Thanks in advance.
hulik