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Old and slow undergraduate mathematics student.


Apr
6
comment Quotient map, quotient topology in Banach spaces
@Rustyn Yes, thanks. I edited.
Apr
6
revised Quotient map, quotient topology in Banach spaces
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Apr
6
asked Quotient map, quotient topology in Banach spaces
Mar
25
awarded  Popular Question
Mar
11
accepted Showing that a series in $l_{\infty}$ converges weakly, given a boundedness condition.
Mar
11
comment Showing that a series in $l_{\infty}$ converges weakly, given a boundedness condition.
Right, it's the other way around. Thank you for the clarifications and the answer!
Mar
11
comment Showing that a series in $l_{\infty}$ converges weakly, given a boundedness condition.
Hi there, thanks. Yeah, the original text refers to "the $w^* $ topology induced by the elements of $l_1$", so I assumed they meant the weak topology since $l_1$ is isomorphic to the dual of $l_{\infty}$. It's Lemma 3 in Joram Lindenstrauss' paper "On complemented subspaces of $m$". Could you tell me what they mean by that?
Mar
10
asked Showing that a series in $l_{\infty}$ converges weakly, given a boundedness condition.
Feb
28
revised Showing that an implicitly defined function is analytic on $(0,\infty)$
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Feb
28
revised Showing that an implicitly defined function is analytic on $(0,\infty)$
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Feb
28
asked Showing that an implicitly defined function is analytic on $(0,\infty)$
Feb
22
accepted $ds=\frac{2|dz|}{1-|z|^2}$ conformal invariant of the disc.
Feb
22
comment $ds=\frac{2|dz|}{1-|z|^2}$ conformal invariant of the disc.
Thank you for your explanation. I'm afraid I don't understand yet. For instance, how do you (in practice) compute the angle between two (tangent) vectors measured by the metric $ds$? And same question for the lengths. Sorry for the trouble.
Feb
19
comment $ds=\frac{2|dz|}{1-|z|^2}$ conformal invariant of the disc.
The book doesn't explicitly mention what is conformal invariance, so my guess is it means that if $z$ and $w$ are related to each other by a Mobius transform then $\frac{2|dz|}{1-|z|^2}=\frac{2|dw|}{1-|w|^2}$. I don't know if I'm interpreting correctly, but if I am, then we need to show that $\frac{1-|z_0|^2}{1-|z|^2}=\frac{1-|w_0|^2}{1-|w|^2}$, right?
Feb
19
comment $ds=\frac{2|dz|}{1-|z|^2}$ conformal invariant of the disc.
Thanks, you're right. How do you show that the correct formula is sufficient to prove the invariance? Do we need to show that $\frac{1-|z_0|^2}{1-|z|^2}=\frac{1-|w_0|^2}{1-|w|^2}$ first? (If so, how?)
Feb
19
asked $ds=\frac{2|dz|}{1-|z|^2}$ conformal invariant of the disc.
Feb
6
comment Why is the complement of the fat Cantor set dense?
Aren't all intervals that remain at stage $n$ the same size? And the length has to tend to zero, because if it didn't, joining $2^n$ of them for $n$ large enough would give you something with measure greater than 1. But I don't know how that helps in showing that one of the removed intervals lies between $x$ and $y$.
Jan
22
comment Saturated measure defined as a supremum of a semifinite measure and countable unions
Would you like me to post the full solution?
Jan
22
comment Saturated measure defined as a supremum of a semifinite measure and countable unions
To my first comment you replied: "I know I can then say that $A\cap E_1$ and $A \cap E_2$ are disjoint subsets of $A$ whose union is all of $A$, and both are elements of $\mathcal{M}$". You don't know if both are elements of $\mathcal{M}$, because locally measurable sets are those whose intersection with any $A$ is in $\mathcal{M}$ as long as that $A$ has finite measure. So you missed something in the infinite case. As for your quandary, you don't need the supremum to be reached. Apply the "$\epsilon / 2^k$" technique. See Folland's textbook.
Jan
21
comment Saturated measure defined as a supremum of a semifinite measure and countable unions
You need to show that in a semifinite measure space, an infinite-measure set can be "approximated" by ever larger measurable sets contained in it.