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seen Dec 10 at 15:48

Math and stuff.


Dec
10
awarded  Caucus
Oct
30
revised Convergence of the sequence $\frac{1}{n\sin(n)}$
deleted 695 characters in body
Oct
30
comment Show that the measure is Lebesque
For instance, take the decimal expansion of your irrational number and truncate it after the $n$th digit behind the decimal point (that is, set all the digits after the $n$th to $0$). The resulting numbers are a rational approximation of your chosen irrational.
Oct
24
comment $\lim _{x\to 2}\:\frac{x}{x^2-4}$ Why using L'hopital rule is wrong?
It's not a limit of the indeterminate form $0/0$.
Oct
24
revised How to determine volume of parallelepiped by 4 points
deleted 27 characters in body
Oct
24
answered How to determine volume of parallelepiped by 4 points
Oct
24
answered Why $L^1$ is not reflexive
Oct
23
answered Proving that $(A^t)^t=A$
Oct
23
comment Show that the measure is Lebesque
What you did until now is only enough for $\mu([a,b))=b-a$ if $b-a\in\mathbb{Q}$. For irrational $b-a$ approximate by rationals and use regularity. Then it follows that $\mu$ is the Lebesgue measure.
Oct
21
comment Show that the measure is Lebesque
No, then its ok.
Oct
21
comment Tonelli-Fubini Theorem for two copies of $\mathbb{N}$ with counting measure
Then it's about interchanging sum and integral.
Oct
20
comment Show that the measure is Lebesque
Ok, but you are implicitly assuming $b-a=m/n$, $m,n\in\mathbb{N}$.
Oct
20
comment Show that the measure is Lebesque
It's not written down correctly, but you are on the right track. Be careful with $\cdots$.
Oct
20
comment Tonelli-Fubini Theorem for two copies of $\mathbb{N}$ with counting measure
It says that you can interchange the sum signs in $\sum_n \sum_m a_{n,m}$ if $a_{n,m}\ge 0$ or $\sum_{n,m} |a_{n,m}|<\infty$.
Oct
20
reviewed Close how to evaluate $ \lim_{x\to 0} \frac{\ln (x)}{1-x} $?
Oct
20
comment Show that the measure is Lebesque
I think I said enough. Translation invariance, additivity, .. play around. You will see. If you really can't solve it, look it up somewhere, this is a standard problem.
Oct
18
awarded  Enlightened
Oct
18
awarded  Nice Answer
Oct
17
reviewed Leave Open Simplify: $\sin \frac{2\pi}{n} +\sin \frac{4\pi}{n} +\ldots +\sin \frac{2\pi(n-1)}{n}$.
Oct
17
reviewed Leave Open How can we explain the discrepancy between $\rightarrow$ (IF-THEN) and $\setminus$ (A-BUT-NOT-B)?