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Jan
28
accepted Theorems which are proven by proving the existence of a formal proof without knowing the formal proof
Jan
28
comment If we have events $E_k, k \in \mathbb{R}$ such that $P(E_k) = 0$ for all $k \in \mathbb{R}$, what is $P(\cup_{k \in \mathbb{R}}E_k)$ equal to?
Or as sangchul pointed, the question may even be meaningless
Jan
28
comment Ideas for approaching set theory when you've already studied higher abstractions?
Elementary set theory from munkres topology
Jan
19
revised Showing that $A+\epsilon I$ is non-singular for $0<|\epsilon|<r$
added 38 characters in body
Jan
19
answered Showing that $A+\epsilon I$ is non-singular for $0<|\epsilon|<r$
Jan
19
awarded  Popular Question
Jan
5
comment Pre measure for an infinite product of measure spaces
wow. Who found out this trick ? By the way, I am forced by the website to wait 15 hours before awarding the bounty. Once more, thanks for your answer.
Jan
5
accepted Pre measure for an infinite product of measure spaces
Jan
5
comment Pre measure for an infinite product of measure spaces
Hi Eric. Thank you a lot for your answer (+225 :)). I recognized the main trick of the proof (using integration to get the sequence $x_1,x_2,...$.All constructions of infinite product measure spaces i saw seem to use topology but your proof doesn't, do you have an explanation why they are using topology?
Dec
24
asked Confusion about the proof of the central limit theorem
Dec
19
accepted smooth functions are dense in the space of bounded continuous functions - why?
Dec
19
comment smooth functions are dense in the space of bounded continuous functions - why?
Ok found one. Thanks a lot +1
Dec
19
comment smooth functions are dense in the space of bounded continuous functions - why?
Thanks for your answer. Any hint on how to construct the $C^{\infty}$ function at the beginning of your answer?
Dec
19
comment Is it possible to write any bounded continuous function as a uniform limit of smooth functions
So boundedness is not actually needed?
Dec
19
asked smooth functions are dense in the space of bounded continuous functions - why?
Dec
18
comment Always real valued complex function
$a=b=c=d=0$ ? $$$$
Dec
17
comment The extension of measures
No it is correct as it is
Dec
17
comment The extension of measures
B has to do in the condition that " B is covered by the sequence E_i"
Dec
17
comment The extension of measures
This is the definitions of $\mu*$
Dec
16
comment Why does $\int_{-L}^{L} \sum_{n=1}^{\infty}a_n\cos \frac{n\pi x}{L}=\sum_{n=1}^{\infty}a_n\int_{-L}^{L}\cos \frac{n\pi x}{L}$
will dominated convergence theorem be useful here ? I can't judge because I don't know the coefficients $a_n$