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Jan
2
revised Growth $\beta X\setminus X$ of a Banach space $X$
added 27 characters in body
Jan
2
comment Growth $\beta X\setminus X$ of a Banach space $X$
suPset. I do know a little bit of elementary metric space theory. Maybe not that much, but at least that...
Jan
2
comment Growth $\beta X\setminus X$ of a Banach space $X$
Ah - I see! But separable spaces are usually not the interesting cases. $L^\infty$? I would be quite surprised if you now tell me all non-separable ones are homeomorphic as well!
Jan
2
revised Growth $\beta X\setminus X$ of a Banach space $X$
added 383 characters in body
Jan
2
comment Growth $\beta X\setminus X$ of a Banach space $X$
The question is giving a Banach space $X$ with a norm $\|\cdot\|_X$, can we enlarge $X$ to make the enlargement with norm $\|\cdot\|_X$ not complete anymore?
Jan
2
comment Growth $\beta X\setminus X$ of a Banach space $X$
But many interesting examples are not separable. Take even a countable tensor product of Hilbert spaces, a bosonic Fock space for instance.
Jan
1
awarded  Custodian
Jan
1
reviewed Close Show $\sum_{n=1}^N e^{i n\theta}.$ is bounded for $ 0< \theta < 2 \pi$, $\forall N \in \{1,2,…\}$
Jan
1
reviewed Reject What do $\pi$ and $e$ stand for in the normal distribution formula?
Jan
1
revised Growth $\beta X\setminus X$ of a Banach space $X$
edited body
Jan
1
asked Growth $\beta X\setminus X$ of a Banach space $X$
Jan
1
awarded  Nice Question
Dec
29
comment Definition of $L^0$ space
Yes, indeed. But, needs a bit of work as you need to mention the topology first. 8-).
Dec
29
comment Definition of $L^0$ space
@Martin: True, I'll modify that. You want to end up with convergence in probability.
Dec
28
answered Definition of $L^0$ space
Dec
28
revised A question from Stein's book, Singular Integral.
added 395 characters in body
Dec
27
answered A question from Stein's book, Singular Integral.
Dec
24
awarded  Popular Question
Dec
23
comment Limit of positive sequence $(f_n)$ defined by $f_n(x)^2=\int^x_0 f_{n-1}(t)\mathrm{d}t$
This proof is actually very slick, but grinding out the details (which is done splendidly) requires some tinkering. I guess there are bigger hammers you can hit the convergence with, but this is truly elementary. I like that. +1.
Dec
21
comment Is this a dirac delta function?
Nice post, shows typical problems with distributions and the order (or even kind of) limits.