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Aug
13
comment Interpretation of $\sigma$-algebra and filtrations (follow-up question)
Thank you for answering an older question, it's always a bit frustrating to get no answers. Since posting this question, my understanding of probability has (luckily) expanded, so this all makes much more sense now. And yeah, the non-constructiveness of the conditional expectations keeps bugging me again and again, looking forward to the day when I'll be able to say that I "got it".
Aug
10
revised How to find eigenvalues of matrix $\begin{bmatrix} 3& a+1\\a+1&3 \end{bmatrix}$
deleted 1 character in body
Aug
7
answered How to find eigenvalues of matrix $\begin{bmatrix} 3& a+1\\a+1&3 \end{bmatrix}$
Aug
7
accepted Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
Aug
7
comment Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
@Berci It appears that other answers are not consistent with your comment (see discussion under Augustin's answer), would you like to elaborate or change it?
Aug
7
comment Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
I suppose my fault was thinking that $[(X,Y)\in A\times B] = [X \in A]\times [Y \in B]$, but then was Berci (in the comments) wrong in saying that $[(X,Y)\in A\times\mathbb R] = [X\in A] \times \Omega$ ?
Aug
7
comment Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
What if we were interested in $[(X,Y)\in A\times B]$? Since you use the same $\omega$ for both $X$ and $Y$ at the same time, wouldn't that be a problem? Or is that again a case where this notation wouldn't work?
Aug
7
comment Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
Thanks (to Stefan Hansen, too), that does make some sense to me, but then, say, what if $Y$ was from a different $\Omega'$? What would the set then look like?
Aug
7
comment Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
I agree and understand, but I do not feel this addresses my problem completely. I've added an edit to the question, which might hopefully be steering my thinking into the right direction.
Aug
7
revised Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
edited title
Aug
7
revised Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
edited title
Aug
7
comment Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
@Berci: true, an actual question on a Q&A site would probably be appropriate. Added, thanks.
Aug
7
revised Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
added the question (duh)
Aug
7
asked Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
Aug
7
comment Types of Mathematical “Sameness”
You are absolutely correct, @m_squared but making sense of (the most notable) examples, or of some kind of hierarchies can be very useful. I tried my best to make this less of a "give me examples of mathematics" question and more a "let's find the pattern that somehow unifies and categorizes the notion of sameness" question. How much I succeeded, of course, is a different story.
Aug
7
comment Types of Mathematical “Sameness”
@Semiclassical thank you, I was so sure something like this had to already exist!
Aug
6
asked Types of Mathematical “Sameness”
Aug
6
comment What does it mean to integrate with respect to the distribution function?
Thanks, ah, so is it simply a notation issue and $\int d\mu = \int \mu(dx)$ by definition?
Aug
6
comment What does it mean to integrate with respect to the distribution function?
This is an older answer, but I'll try nonetheless: how is one to understand $\int_\mathbb{R} x \mu_{F}(dx)$? I've never seen that notation and am unsure of what it's supposed to mean.
Aug
4
awarded  Popular Question