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Math and stuff.


1d
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 $0/0$.
1d
revised How to determine volume of parallelepiped by 4 points
deleted 27 characters in body
1d
answered How to determine volume of parallelepiped by 4 points
1d
answered Why $L^1$ is not reflexive
2d
answered Proving that $(A^t)^t=A$
2d
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
18
reviewed Close What does a day in the life of a mathematician look like?
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)?
Oct
17
reviewed Close Why do we need an open set to define differentiability?
Oct
17
reviewed Leave Closed How to prove that the integration contour of one integral is the subset of the other integral?