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Jul
28
comment f:Lebesgue measurable function ⇆ ∀ε>0, ∃g:continuous function s.t. λ({x|f(x)≠g(x)})<ε
The "$\Rightarrow$" implication seems to be Lusin's theorem.
Jul
28
revised Singular Lebesgue-Stieltjes measure
edited tags
Jul
28
revised Consider two singular measures $ m$ and $v$ and $v$ is absolutely continuous with respect to $m$ show that $v=0$
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Jul
28
revised Relative entropy between singular measures
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Jul
28
comment $\left\| A \right\| \le \varepsilon \Rightarrow \left\| {\mathop A\limits^{\_\_} } \right\| \le \varepsilon$
$\|\overline{A}\|=\|A\|=\|A^*\|$, so yes.
Jul
28
revised Weak convergence, $L^{2}$
retag
Jul
28
answered How to prove these inequalities using Fourier analysis methods
Jul
28
answered Prove by induction that $\sum_{k=1}^{n} k^3 = \bigg( \sum_{k=1}^{n}k\bigg)^2$
Jul
25
revised Is this problem wrongly built? Or is there a solution which I don't know how to arrive at?
added 90 characters in body
Jul
25
answered Is this problem wrongly built? Or is there a solution which I don't know how to arrive at?
Jul
25
comment Help me proving $x^{\frac{1}{x}} \geq \frac{1}{3}$
For $x\ge 1$ we have by monotonicity of $\log(x)$, $x^{1/x}=e^{\log(x)/x}\ge e^{\log(1)/x}=1>1/3$. So you can set $b=1>1/2$.
May
27
answered Show that the closed ball $B[x,1]$ in $c_0$ is not compact.
May
27
answered $f(n) = n^{\log(n)}$, $g(n) = log(n)^{n}$ is $f\in O(g(n))$?
May
27
comment Is $[X,Y] \neq 0$ the sufficient condition of $e^{X+Y} \neq e^Xe^Y$?
Your identity is generally false. See Baker-Campbell-Hausdorff formula.
May
27
revised Convergence of the sequence $\frac{1}{n\sin(n)}$
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Mar
19
awarded  Sportsmanship
Mar
18
revised Solving an equation $\pmod {13}$
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Mar
18
answered Solving an equation $\pmod {13}$
Mar
18
reviewed Leave Open The n-envelope problem
Mar
18
reviewed Close Most efficient way to learn mathematics