Let's say I have a sequence of random variables [math] \{

>>8476431
I'm not so sure about that. I would say that that convergence shows that probability of existence of such index j tends to 1.
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>>8476431
No.

>>8476431
wouldn't you want to show that the probability is 0? Convergence doesn't mean that it will become 0 and I don't even know for what variable that you take to infinity you would have convergence.

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>>8476493
So here's the problem I'm having. I'm trying to prove that a Brownian motion is not a BV "function".

I got this idea to take a random partition, and then showing that by adding points to the partition, the total variation gets larger.

But here I need to have that there is at least one interval where the increment is negative, in an interval with positive incrementation.

I'm trying to show this by showing that the probability we won't find this goes to zero, as we make the partition of the sub-interval smaller.

The pic should explain it a bit more.

Any suggestions how I should word this?

>>8476558
>partition of the sub-interval smaller
I mean to say: we make the mesh of the partition smaller by refining the partition.

>>8476673
Holy fuck, thank you!!!

What book is this from?