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Disgruntled with physics, now a student of mathematics.


Sep
15
awarded  Popular Question
Aug
26
comment From $\left\lVert \sup_{M>M_0} \left| \sum_{k=M_0}^M f_k \right| \right\lVert_2 < \epsilon$ show convergence a.e. of the series.
That's brilliant, thanks.
Aug
26
comment From $\left\lVert \sup_{M>M_0} \left| \sum_{k=M_0}^M f_k \right| \right\lVert_2 < \epsilon$ show convergence a.e. of the series.
Thank you for your answer. I'm trying to understand it... Why does $x\in E_t$ imply $\sup_{M>M_0}|F_{M}-F_{M_0}|>2^{-t-1}$ ?
Aug
26
revised From $\left\lVert \sup_{M>M_0} \left| \sum_{k=M_0}^M f_k \right| \right\lVert_2 < \epsilon$ show convergence a.e. of the series.
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Aug
26
asked From $\left\lVert \sup_{M>M_0} \left| \sum_{k=M_0}^M f_k \right| \right\lVert_2 < \epsilon$ show convergence a.e. of the series.
Aug
18
awarded  Yearling
Aug
13
comment Is it possible for a function to be in $L^p$ for only one $p$?
I'm not following, is $\frac1{x^{1/p}\log^2(x^{1/p})}$ the inverse of $\left(\frac1{x\log^2x}\right)^p$ ?
Aug
12
accepted How to show $ \left(\frac{1-x}{2}\right)^p+\left(\frac{1+x}{2}\right)^p \leq \frac{1+x^p}{2}$
Aug
12
asked How to show $ \left(\frac{1-x}{2}\right)^p+\left(\frac{1+x}{2}\right)^p \leq \frac{1+x^p}{2}$
Aug
12
accepted rationalwiki on “Extraordinary claims require extraordinary evidence”
Aug
11
asked rationalwiki on “Extraordinary claims require extraordinary evidence”
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
29
comment The set of $x$ where a sequence convergences in terms of set operations
You're right. Thanks again.
Jun
29
accepted The set of $x$ where a sequence convergences in terms of set operations
Jun
29
comment The set of $x$ where a sequence convergences in terms of set operations
thanks a lot. I'm still trying to internalize the proof; I understand the difference between uniform and pointwise continuity. The distinction in the proof is very subtle for me, since between the two intersections in your answer we could still insert a $\bigcup_{n_k\in\mathbb{N}}$, meaning that there exists $n_k$ (the one that was constructed) such that...
Jun
29
comment The set of $x$ where a sequence convergences in terms of set operations
@yoyo Thanks. So I thought. But then I don't understand the proof of Egorov's theorem: en.wikipedia.org/wiki/Egorov's_theorem#Proof Isn't the complement of that set $B$ at the end precisely a set like the one in my post?
Jun
29
asked The set of $x$ where a sequence convergences in terms of set operations
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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