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I fill in "About Me" sections from time to time.


1d
revised Why this power inequality for sums of real numbers holds?
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2d
answered Given a set $A$, how do I prove that there exists a set of all sets $x$ such that $\bigcup x=A$?
2d
answered Assume c ∈ (0, 1) is given. What is inf {c^n |n ∈ N }?
2d
answered To check whether series is convergent or not
2d
answered Why this power inequality for sums of real numbers holds?
2d
comment Is i holomorphic over the whole complex plane?
Clearly that example shows that $f(z) f(\bar{z}) \neq |f(z)|^2$ in general or even for entire functions. But it doesn't seem to me that that not holding would have any impact on a function not having a derivative.
2d
answered Is i holomorphic over the whole complex plane?
2d
answered Prove ${x:d(x,p) < d(x,q)}$ is open in metric space $X$
2d
answered Does the sequence $( n^{1/n} -1)$ belong to any $\ell^p$ space?
Dec
15
revised If a sequence $f_n$ is bounded in $L^2$ and converges to zero a.e., then $f_n\to 0$ in $L^p$ for $0<p<2$
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Dec
15
revised Any finite set is compact; what exactly is a finite set?
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Dec
15
comment Any finite set is compact; what exactly is a finite set?
There is no reason to downvote this question.
Dec
15
answered Any finite set is compact; what exactly is a finite set?
Dec
15
comment If a sequence $f_n$ is bounded in $L^2$ and converges to zero a.e., then $f_n\to 0$ in $L^p$ for $0<p<2$
No problem. I edited my answer quite a bit after I realized I was using Holder in a more convoluted way. I forgot $g=1$ is good enough. Also, I was using $|f_n| \geq 1$, which is an assumption we can make because the dominated convergence theorem takes care of $|f_n| \leq 1$.
Dec
15
revised If a sequence $f_n$ is bounded in $L^2$ and converges to zero a.e., then $f_n\to 0$ in $L^p$ for $0<p<2$
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Dec
15
answered If a sequence $f_n$ is bounded in $L^2$ and converges to zero a.e., then $f_n\to 0$ in $L^p$ for $0<p<2$
Dec
12
comment Breaking a Function in $L^{\infty}[0,1]$
What about $g=h=f$?
Dec
11
reviewed Approve Best book for a casual pure mathematician?
Dec
11
answered If L(P, f) = U(P, f), prove that f is a constant function on [a, b]
Dec
10
comment Find all functions: $\left ( \int \frac{dx}{f(x)} \right )\left ( \int f(x)dx \right )=c$
The problem is ill-defined unless you specify lower bounds $a$ and $b$ or if you are looking for solutions $f(x)$, $a$, and $b$ satisfying the above.