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visits member for 4 years
seen May 18 '13 at 10:40

On extended leave from the site. I visit occasionally, but irregularly, mostly without logging in. For the time being it is impossible to predict if and when I will find the time to contribute again.


Feb
3
comment Proof of inequality involving surds
There were a few edits that seem to have changed/corrected mathematical content in the OP. I don't think it's a good idea to do that and reviewers should look more closely...
Feb
3
comment Non-isomorphic atomless Boolean algebras
For me the measure algebra of a measure space is the algebra of measurable sets modulo the ideal $\mathcal{N}$ of null sets. Thus, $\mathfrak{A} = \mathfrak{L}/\mathcal{N} \cong \mathfrak{B} / (\mathfrak{B} \cap \mathcal{N})$ has cardinality $\mathfrak{c}$. Otherwise ccc wouldn't tell $\mathfrak{A}$ and $\mathfrak{B}$ apart, would it? :)
Feb
3
comment Is Topology an important class to take before Functional Analysis?
Thanks for the feedback, that's very nice to hear and I really appreciate it. Good luck with your further studies!
Feb
3
reviewed Reject Is A∨¬A a tautology when there is a proof (by contradiction)?
Jan
4
awarded  Yearling
Dec
26
comment Is Hom$(G,-)$ left exact if morphisms are required to be continuous?
Hi Ben, I just stumbled over this thread: in view of the accepted answer, maybe you're interested in having a look at my expository paper on exact categories where I give a hands-on approach to Quillen's theory. Best wishes and a happy New Year, Theo
Dec
23
reviewed Leave Open How you review the contents which you have learnt several month before?
Dec
23
revised banach-spaces wiki excerpt
removed unnecessary symbols
Dec
23
revised banach-spaces wiki excerpt
I removed the specification of the ground field since there is absolutely no reason to exclude p-adic Banach spaces. There's also no need to define Cauchy sequences here.
Dec
20
reviewed Close multiple choice question on holomorphic functions
Dec
20
reviewed Reject Mathematical difference between white and black notes in a piano
Dec
20
comment Inner regularity property of Radon measures in metric spaces
You understand Michael's answer correctly. You can find proofs in many places, for example Theorem 3.2 in Parthasarathy's Probability Measures on Metric Spaces or Theorem 17.11 of Kechris's Classical Descriptive Set Theory.
Dec
20
comment Inner regularity property of Radon measures in metric spaces
I see. Here's the idea: The example of a non-tight Radon measure on an uncountable disjoint union of $\mathbb{R}$ I linked you to can be modified to use the Cantor set with the "coin-flipping measure" instead of $\mathbb{R}$. Thus the task is essentially reduced to find a closed subspace of a metric space which is homeomorphic to an uncountable disjoint union of Cantor sets. This can be done using this construction and a locally finite disjoint family of open sets (and some effort). I'm not so sure if the actual construction is all that enlightening.
Dec
19
awarded  Enlightened
Dec
19
awarded  Nice Answer
Dec
19
comment Inner regularity property of Radon measures in metric spaces
I didn't work it out in full detail, but I think that one can use the example I alluded to above to show that on every non-separable complete metric space without isolated points there is an outer measure as in Evans-Gariepy, but that the associated measure (from Carathéodory) will not be tight while satisfying all your conditions. On the other hand, one can always construct a tight version of it which will fail to be outer regular.
Dec
19
reviewed Reject Inequality involving expectation
Dec
19
comment Weak-to-weak continuous operator which is not norm-continuous
@Mike: that's my favorite example, too :-) It may be worth adding that the summation functional is adjoint to the limit functional on $c$ (convergent sequences). That is, if you view $\ell^1$ as the dual space of $c$ via the pairing $\langle x,y \rangle_{\ell^1,c} = \left(\sum x_n\right) \lim y_n + \sum x_n y_n$ then $T$ is adjoint to $S(y) = (\lim y_n) \cdot e_1$.
Dec
19
comment Inner regularity property of Radon measures in metric spaces
What kind of spaces are you interested in? Do you care about large spaces (not $\sigma$-compact)? Would you mind adding completeness? Have you considered the example of Lebesgue measure times counting measure on the reals times the discrete reals (it has two incarnations: one is inner regular but not outer regular and the other is outer regular but not inner regular)?
Dec
19
reviewed Approve Do there exist any odd prime powers that can be represented as $n^4+4^n$?