Reputation
4,110
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
2 11 30
Impact
~54k people reached

Mar
10
comment A doubt in Probability essentials by Protter
@user3503589: There is probably a mistake in the print. What is certain is, that once you leave the absolute values you have an equality, and he is, essentially, arguing that if you drop the absolute values the estimate grows. Which seems to be false. But you can keep the absolute values and the argument goes through.
Mar
10
answered A doubt in Probability essentials by Protter
Mar
10
comment A doubt in Probability essentials by Protter
What is the definition of $p_{\omega}$? Is $\Omega$ a countable space here?
Mar
9
comment Measure of $E$ is the limit of the measure of the open set $\mathcal{O}_n$
@dragon: yeah, precisely what I meant. I'm glad you got it.
Mar
9
revised Measure of $E$ is the limit of the measure of the open set $\mathcal{O}_n$
added 5 characters in body
Mar
9
comment Measure of $E$ is the limit of the measure of the open set $\mathcal{O}_n$
@dragon: There is no reverse inequality needed to prove. Since $E=\bigcap_{n=1}^{\infty}O_{n}$ and $O_{n}\supseteq O_{n+1}$ for all $n$, then $m(E)=\lim_{n\to\infty}m(O_{n})$ by convergence of measure since $m(O_{1})<\infty$ as $E$ was compact. Are you aware of the result that if $O_{n}\supseteq O_{n+1}$ for all $n$ and $E=\bigcap O_{n}$, then $m(E)=\lim_{n\to\infty}m(O_{n})$ if $m(O_{1})<\infty$?
Mar
9
revised Measure of $E$ is the limit of the measure of the open set $\mathcal{O}_n$
added 483 characters in body
Mar
9
answered Measure of $E$ is the limit of the measure of the open set $\mathcal{O}_n$
Jan
6
awarded  Yearling
Dec
21
awarded  Constituent
Dec
12
awarded  Caucus
Oct
20
comment The Complex projective space is homeomorphic to the n-sphere
What definition of the complex projective space do you use?
Oct
15
comment Question about the closure of a set
@Luis: That sequence does not have a limit.
Oct
15
answered Question about the closure of a set
Oct
15
reviewed Approve Question about the closure of a set
Oct
2
comment The set of rational numbers in the interval $(0,1)$ cannot be expressed as the intersection of a countable collection of open sets
@YiorgosS.Smyrlis. Got it. Thanks.
Oct
2
comment The set of rational numbers in the interval $(0,1)$ cannot be expressed as the intersection of a countable collection of open sets
@YiorgosS.Smyrlis: Why do $U_{n}$ have to be dense? The statement only says that rationals in $(0,1)$ can not be expressed as a countable intersection of open sets, not necessarily dense ones.
Sep
30
awarded  Explainer
Sep
28
answered Prove that $\{x_{n}\} \subseteq A$ a Cauchy sequence $\Rightarrow$ $\{f(x_{n}\}\} \subseteq y$ is a Cauchy sequence.
Sep
12
comment Why is differential geometry called differential geometry?
Usually the Riemannian metric of a smooth manifold captures it's geometric properties such as curvatures and angles. One doesn't need to integrate on the manifold to capture these notions.