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comment Representation of a linear functional Lipschitz in total variation
Thanks, this example works perfectly. No weak continuity assumptions, I'm also not sure why did I go for Borel space at the time I've asked this question, as I do not seem to use this structure at all. Do you think weak continuity would make this true, or just harder to find a counterexample (in case you have already thought of that)?
1d
accepted Representation of a linear functional Lipschitz in total variation
May
3
comment Representation of a linear functional Lipschitz in total variation
The answer below does not seem to be correct according to its author.
May
1
awarded  Notable Question
Apr
28
revised Representation of a linear functional Lipschitz in total variation
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Apr
25
awarded  Popular Question
Apr
24
asked Minimizing the average
Apr
24
revised Can anyone clarify the meaning of zero content?
added 61 characters in body
Apr
23
comment What is the optimal path between $2$ fixed points around an invisible obstructing wall?
Can you tell where do you know this puzzle from?
Apr
11
comment Decaying way to compute sample mean
I think an easier check is to see that variance of $s_n$ has a positive limit in the end, whereas if $a_n = \frac1n$ as in usual sample mean, then variance converges to zero.
Apr
11
revised Decaying way to compute sample mean
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Apr
9
comment Compact but not measurable
Three upvotes? ${}$
Apr
9
asked Decaying way to compute sample mean
Apr
9
awarded  Favorite Question
Apr
8
comment Extension of Kakutani's fixed point theorem.
One obvious condition I can think of is: any point from the boundary is mapped to the inside.
Apr
8
comment Approximate partition of unity by characteristic functions
By characteristic functions you mean indicators, that equal $1$ on the set and $0$ otherwise? If yes, which kind of convergence are you talking about? Let's say, on real line $v_1 = \frac12(1 + \sin x)$ and $v_2 = 1 - v_1$, how would you construct a sequence of sets $E_{1j}$ that converge to $v_1$?
Apr
8
awarded  integration
Apr
5
awarded  Socratic
Apr
4
comment Coarsest filtration
$\mathcal F$ here is the $\sigma$-algebra on the original probability space, so yes, $\xi_t$ is $\mathcal F$-measurable for all $t$. W.r.t. existence, the shift process on $\omega$ satisfies all required properties. However, it is a very expensive process in terms of filtration.
Apr
4
comment Coarsest filtration
@TheBridge: I still don't get it, do you mean that for such process there does not exist the coarsest Markov super-pricess?