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visits member for 3 years, 11 months
seen 21 hours ago

Oct
17
comment Understanding change of variable in measure spaces
Thank you! I was actually going to write it for simple functions as an answer in response to your comment. Regarding your comment: what does extend by continuity mean? Isn't it enough that simple functions are dense?
Oct
13
comment Trying to understand $\mathbb{Q} / \mathbb{Z}$
$b$ might work?
Oct
13
comment Trying to understand $\mathbb{Q} / \mathbb{Z}$
Thank you! I'm just never sure whether what I do is right...
Oct
13
comment A question about the tensor product of $\mathbb{Q}$
@KCd: thank you, will do!
Oct
13
comment A question about direct sums and products of modules
@HansLundmark: I'm glad I'm not the only one who writes stupid things.
Oct
13
comment Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
@ShaunAult: thanks! I'm not sure I understand why I cannot treat $1$ as a basis though... Could you tell me more please?
Oct
13
comment A question about the tensor product of $\mathbb{Q}$
So just to make sure I understand this: $a \otimes b + c \otimes d$ is also a simple tensor?
Oct
13
comment A question about direct sums and products of modules
Thank you! Of course : / And what is your answer to my question 1?
Oct
11
comment Characterisation of compact subsets of Banach spaces
@t.b.: I think every subset is equicontinuous: for any $\varepsilon$ choose $\delta := 1 / 2$ then $|x(n) - x(n^\prime)| = 0 < \varepsilon$ if $|n - n^\prime| < \delta$.
Oct
11
comment Characterisation of compact subsets of Banach spaces
@t.b.: thanks! I think I've corrected it. Maybe it's your browser's cache if you can still see $\mathbb{N}_\infty$?
Oct
11
comment Characterisation of compact subsets of Banach spaces
@martini: thanks! That's clever : )
Oct
11
comment Space of bounded continuous functions is complete
Thanks for your help!
Oct
10
comment Seeking a layman's guide to Measure Theory
I think active reading should happen naturally, without the need to be promoted. I'm driven and curious. Reading something that spells out nothing is frustrating and tiring to me.
Oct
10
comment Seeking a layman's guide to Measure Theory
Yes it does! I read slowly. I read, think, then discover that what I thought was actually right and if it wasn't I get corrected. If I read an-everything-is-obvious-sort-of-book it's an almost complete waste of time because I have no way of checking whether I actually understood what I just read.
Oct
9
comment Construction of an non-measurable set
My pleasure! Actually, $C$ is only in $[0,1]$ if you take $B$ to be $[0,1]$ or in your case $[0,1]^N$. That's how the Vitali set is usually constructed. I'll correct my answer to use $B = [-1,1]^N$ as in your exercise.
Oct
9
comment Construction of an non-measurable set
Yes! That's right! I added more details to my answer.
Oct
9
comment Space of bounded continuous functions is complete
@t.b.: my mentor (if I may still call you that) just virtually smacked my fingers with a ruler. I won't use the word limit again without saying which limit I'm talking about. : )
Oct
7
comment A question about the nilradical
Thank you, @AmiteshDatta !
Oct
6
comment The ring of germs of functions $C^\infty (M)$
Hi @GeorgesElencwajg: Thank you!! Of course!
Oct
6
comment A question about the nilradical
Can I ask you one more question? Is $M + (ab) = (M + (a))(M + (b))$? i.e. is it also true that $(M + (a))(M + (b)) \subset M + (ab)$?