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visits member for 2 years, 6 months
seen Jul 20 at 22:14

Doing math.


May
31
comment Integrals and Dirac delta measures
@rosie: We can always do such a composition $X=X^{+}-X^{-}$ where $X^{+}=\max\{X,0\}$ and $X^{-}=-\min\{X,0\}$. Then by using the previous step (since both $X^{+}$ and $X^{-}$ are non-negative and measurable) we get $\int X\,d\delta_{k}=\int X^{+}\,d\delta_{k}-\int X^{-}\,d\delta_{k}=X^{+}(k)-X^{-}(k)=X(k)$.
May
31
revised Integrals and Dirac delta measures
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May
31
comment Integrals and Dirac delta measures
Yeah, it looks correct now.
May
31
revised Integrals and Dirac delta measures
added 639 characters in body
May
31
answered Integrals and Dirac delta measures
May
31
comment Integrals and Dirac delta measures
Should the right-hand side be $X(0)$? Or at what point is that dirac measure standing on?
May
31
awarded  Citizen Patrol
May
31
comment a question on subsets of rational number and analysis.
This question seems to be an identical duplicate from the above one.
May
31
comment Prove that $\sin(x+\frac{\pi}{n})$ converges uniformly to $\sin(x)$.
@Belgi: where in the definition of uniform convergence does $\delta$ appear?
May
31
comment Is the box topology good for anything?
Sure; and thanks for doing it. Such things which require correction are important to point out:)
May
31
comment Is the box topology good for anything?
@SamL. Thanks for pointing that out. That identity would have not been mandatory but rather a shortcut: but clearly it is exactly as you pointed out. I edited it once again, maybe this should fix the problem?
May
31
revised Is the box topology good for anything?
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May
31
comment Is the box topology good for anything?
I edited the answer accordinly. It is fine as it is now too (although less practical), but I will also try to find some conditions where they coincide. But if nothing else, my answer is atleast an elaboration of dfeuer's comment as I promised:)
May
31
revised Is the box topology good for anything?
Huge edit.
May
31
revised Is the box topology good for anything?
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May
31
comment Is the box topology good for anything?
@t.b.: good point, there might be a detail or an extra assumption that I have overlooked or forgotten. I will try to find this from somewhere. For now it seems that $\tau_{\sup}\subset$ Box topology.
May
31
revised Is the box topology good for anything?
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May
31
answered Is the box topology good for anything?
May
31
comment Totally disconnected implies base of closed sets?
Sure. +1 for a nice answer.
May
31
comment Continuous images of compact sets are compact
The proof looks good.