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1d

comment 
Limit inferior of Borel functions
Thanks. For anyone else who is interested, it's at math.stackexchange.com/questions/1380337/…. 
2d

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Limit inferior of Borel functions
And if you post it on Math.SE, would you please leave a comment here to say you have done so, and include a link? Also please include the string "@nate" in your comment so that I get notified. 
2d

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Limit inferior of Borel functions
I suggest you post this on math.stackexchange.com, which accepts math questions without the "research level" requirement. If you do, I will answer it. (I believe the answer is "not necessarily".) 
Jul 30 
comment 
Are smooth solutions to a PDE dense in the space of $L^2$ solutions to the PDE?
@OtisChodosh: The question does specify "smooth coefficients", though. 
Jul 29 
comment 
integrability of Brownian motion stopped at some stopping time
Unless I'm misunderstanding, isn't $\tau = 0$ almost surely? It seems to me that the stopping time will occur at least as soon as $S_t > 0$ and $B_t \le 0$, which happens immediately after time 0. 
Jul 27 
comment 
Baire Category Theorem for complete uniform spaces
@JonathanGleason: FYI, in your "counterexample" the sequence $x_m$ doesn't converge to 0 in this topology. For instance, the set $U = \{ x : x(n) < \frac{1}{2n}, n = 1,2,\dots\}$ is an open neighborhood of 0 but contains none of your $x_m$. But I'm fairly sure it's not Cauchy either. 
Jul 26 
comment 
Which journals publish applied mathematics with mostly pure mathematics content?
@Suvrit: Well, I stand corrected. Obviously I wasn't that referee :) 
Jul 26 
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Which journals publish applied mathematics with mostly pure mathematics content?
I don't think I would necessarily assume that the "applied content" automatically makes the paper unsuitable for a pure math journal. If the mathematical results are of interest by themselves, then explaining how they are used in an applied context could only increase the interest, I would think. 
Jul 24 
comment 
Existence of a countable linear combination with positive coefficients
Oh, I see. Thanks. 
Jul 24 
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Existence of a countable linear combination with positive coefficients
I know a couple of "usual" ways to make $c_{00}$ into a locally convex space, but unless I have got my definitions completely wrong, they aren't complete... 
Jul 23 
answered  Where can I find a copy of Moussatat's 1976 thesis “On the Asymptotic Theory of Statistical Experiments and Some of Its Applications”? 
Jul 23 
answered  Is a specific sequentially closed subset of $M([0,1])$ closed? 
Jul 22 
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Analytic Number Theory without Pigeonhole Principle
@AlexDegtyarev: Isn't "do this without that" the whole idea of reverse mathematics? I think this particular question is too broad for this site, but in general it's a legitimate sort of question to ask. 
Jul 22 
comment 
Poincare inequality for connected Lie groups
A standard way to abstract "integral of the gradient" is with a Dirichlet form. 
Jul 22 
comment 
A problem in functional calculus
As a start, is it true for $2 \times 2$ matrices? 
Jul 21 
awarded  Popular Question 
Jul 18 
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The existence of stationary measures for certain Markov process
For example, an iid sequence drawn from a continuous distribution does not satisfy them. Usually when dealing with continuousstate models, you have to introduce a topology on the state space to be able to say anything useful. 
Jul 18 
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The existence of stationary measures for certain Markov process
Maybe you can be more explicit about your definitions. Do you really want your state space to be completely general (e.g. any measurable space) or are you willing for it to be, e.g., standard Borel? And what do you want "positive recurrence" and "communication" to mean, exactly? If you mean "for all $x$ we have $E_x[\tau_x] < \infty$" and "for all $x,y$ we have $P_x(\tau_y < \infty) = 1$" then these are extremely strong assumptions that are probably not satisfied by very many useful examples. 
Jul 16 
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Is the set of the convolutions of twopoint measures dense in the set of all measures?
I don't understand the down and closevotes here. Although the question has a simple statement, it doesn't seem to me to be trivial. 
Jul 15 
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Is there an $\infty$ version of the Wasserstein distance between two distributions?
Is it clear, for instance, that your $W_\infty$ is a metric? 