- (Un-)Countable union of open sets - Mathematics Stack Exchange
A remark: regardless of whether it is true that an infinite union or intersection of open sets is open, when you have a property that holds for every finite collection of sets (in this case, the union or intersection of any finite collection of open sets is open) the validity of the property for an infinite collection doesn't follow from that In other words, induction helps you prove a
- functional analysis - Where can I find the paper Un théorème de . . .
J P Aubin, Un théorème de compacité, C R Acad Sc Paris, 256 (1963), pp 5042–5044 It seems this paper is the origin of the "famous" Aubin–Lions lemma This lemma is proved, for example, here and here, but I'd like to read the original work of Aubin However, all I got is only a brief review (from MathSciNet)
- optimization - Minimizing KL-divergence against un-normalized . . .
Minimizing KL-divergence against un-normalized probability distribution Ask Question Asked 1 year, 4 months ago Modified 1 year, 4 months ago
- sequences and series - (Un)equivalence of two definitions $R . . .
You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
- Homotopy groups U(N) and SU(N): $\\pi_m(U(N))=\\pi_m(SU(N))$
Yes, that's right, and yes, $\pi_1$ should be $\mathbb {Z}$ for all $N$ in the table
- modular arithmetic - Prove that that $U (n)$ is an abelian group . . .
Prove that that $U(n)$, which is the set of all numbers relatively prime to $n$ that are greater than or equal to one or less than or equal to $n-1$ is an Abelian
- Mnemonic for Integration by Parts formula? - Mathematics Stack Exchange
The Integration by Parts formula may be stated as: $$\\int uv' = uv - \\int u'v $$ I wonder if anyone has a clever mnemonic for the above formula What I often do is to derive it from the Product R
- probability - Suppose that $U1, U2, . . . , Un$ are iid $U (0,1)$ and $Sn . . .
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