3,990 reputation
11545
bio website
location
age 25
visits member for 3 years, 9 months
seen 19 hours ago

Nov
12
comment Prove $\sum_{n=1}^{\infty} n \mu(A_n) = \sum_{n=1}^{\infty}\mu(B_n) = \sum_{n=1}^{\infty} \mu(E_n)$
Yes, the triple equality doesn't holds in general. I misread the thing, wanted that can to be some other can't. Thank you for the clarification.
Nov
12
comment Prove $\sum_{n=1}^{\infty} n \mu(A_n) = \sum_{n=1}^{\infty}\mu(B_n) = \sum_{n=1}^{\infty} \mu(E_n)$
@DanielFischer I think you mean: "but it can't be that..." at the end of the integrals solution.
Nov
12
awarded  Popular Question
Nov
11
comment what is the cardinality of a Null set?
What kind of null set?
Nov
10
revised Composition of measureable function with continuou function in $L^2[0,1]$
Formatting.
Nov
7
comment Is there a rationality-preserving order isomorphism between $\mathbb{Q}$ and two disjoint open intervals?
If there's an order preserving map between negative rationals (positive rationals) and rationals, one idea is to: send negative rationals to rationals to first interval, and positive rationals to rationals to second interval.
Nov
5
revised Give a counterexample to show that $(AB)^{-1} \neq A^{-1}B^{-1}$
edited title
Nov
4
comment Can basis vectors have fractions?
@tokola If the vectors in the basis you found are just scalar multiples of the vectors in the solution from the book you should end up with the same diagonal matrix that they have. So maybe you made a mistake when calculating $P^{-1}AP$ or when calculating the power you mention. By the way, funny nickname.
Nov
4
revised Prove that g(y)>0 for all y in the real numbers
This has nothing to do with proof theory.
Nov
4
comment What is the negation of the statement $f=0$ almost everywhere?
Yes, $f=0$ almost everywhere implies $f$ measurable.
Nov
4
comment What is the negation of the statement $f=0$ almost everywhere?
I pointed that because I recall that $f = 0$ almost everywhere meant the set where $f$ is not $0$ has $0$ measure. Nothing is said about the measurability of $f$. Then what I wrote.
Nov
4
comment What is the negation of the statement $f=0$ almost everywhere?
I'd say: the set $\{x:f(x)\neq 0\}$ is not measurable or there's a set $E$ with positive measure such that $f(x)\neq 0$ for each $x\in E$. This negation includes for example the characteristic function of a non measurable set. Of course what you say is fine if the function is presupposed to be measurable.
Nov
4
comment Triangle inequality
Related
Nov
4
revised Let $V$ be a finite dimensional real vector space and let $A:V\to V$ be a linear map such that $A^2=A$
added 143 characters in body
Nov
3
answered Let $V$ be a finite dimensional real vector space and let $A:V\to V$ be a linear map such that $A^2=A$
Nov
1
comment On Fatou's Lemma
Limit may not always exist.
Oct
31
awarded  Popular Question
Oct
29
comment A sequence of truncates of $f$
I formatted a bit your post. Still $f_A$ isn't well defined.
Oct
29
revised A sequence of truncates of $f$
Formatting
Oct
29
comment How to factor $x^{4}-22x^{2}+9$ over real numbers?
This question is far more specific than what the original title suggested.