3 days ago · Mathematics Stack Exchange is a platform for asking and answering questions on mathematics at all levels.

Jun 4, 2012 · 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 …

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Nov 12, 2015 · 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 …

Yes, it is more natural to use the determinant, see the duplicate. There the same doubt was mentioned, that the proof with centers is not so "insightful". On the other hand, the definition of a center is easy …

Nov 2, 2022 · I meant it to read: P (S_1 ≤ t) P (S_n ≤t). The product of those probabilities given the assumption is true.

Nov 11, 2018 · 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 …

Jan 5, 2016 · The "larger" was because there are multiple obvious copies of $U (n)$ in $SU (n) \times S^1$. I haven't been able to get anywhere with that intuition though, so it ...

Dec 15, 2019 · Using reduction formula for $\sin (x)$ we have: $$\int_ {0}^ {\frac {\pi} {2}}\sin^ {n}\left (x\right)dx=\frac {n-1} {n}\int_ {0}^ {\frac {\pi} {2}}\sin^ {\left (n-2 ...