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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
comment 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
comment 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
comment 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
comment 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
comment 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
comment 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 continuous-state models, you have to introduce a topology on the state space to be able to say anything useful.
Jul
18
comment 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
comment Is the set of the convolutions of two-point measures dense in the set of all measures?
I don't understand the down- and close-votes here. Although the question has a simple statement, it doesn't seem to me to be trivial.
Jul
15
comment Is there an $\infty$ version of the Wasserstein distance between two distributions?
Is it clear, for instance, that your $W_\infty$ is a metric?