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Mar
12
awarded  Popular Question
Mar
12
awarded  Nice Question
Mar
11
comment How to explain brackets to young students
@SimonS thank you, I remember that board as a concept, missed its actual start! Will do.
Mar
11
comment How to explain brackets to young students
@Surb Ha, I like the magic number idea. I shall use that!
Mar
11
asked How to explain brackets to young students
Mar
9
answered Find the inner product under which is the following base orthonormal
Mar
9
comment Find the inner product under which is the following base orthonormal
Sorry for editing the question like that, I originally misunderstood what the person that brought this to my attention said and posed a completely wrong question.
Mar
9
revised Find the inner product under which is the following base orthonormal
added my progress
Mar
9
accepted Two quick eigenvalues & complex numbers questions
Mar
9
asked Find the inner product under which is the following base orthonormal
Mar
8
asked $ X_n = 2 Y_n + Y_{n+1} $ (non)Markov Chain
Feb
17
awarded  Notable Question
Nov
12
comment Why does $\sigma (X_t) \subset \sigma (X)$ hold?
I meant the definition of a (measurable) cylinder. I still don't see why $X_t^{-1}(B_t)=X^{-1}(B)$. Please comment a bit more on that.
Nov
12
accepted Why does $\sigma (X_t) \subset \sigma (X)$ hold?
Nov
11
awarded  Yearling
Nov
10
comment Why does $\sigma (X_t) \subset \sigma (X)$ hold?
Thanks, answers cleared my questions up, sadly, I still need a (hopefully) small nudge. Measurable cylinders are where most of my problems with probability theory mostly occur. a) do we agree on the definition that $B_t=S_t$ except for finitely many $t$'s? If so then is $B$ such a set? and finally b) Why does $X_t^{-1}(B) = X^{-1}(B)$? I am not even sure what $X_t^{-1}(B)$ means - since B seems to be a collection of elements of $\prod S_t$.
Nov
10
comment Why does $\sigma (X_t) \subset \sigma (X)$ hold?
Thanks, this answer is still quite cryptic to me though. A couple of questions: a) $X_t$ is measurable in what sense? $\forall B\in\mathcal{S}_t$ we have $X^{-1}_t\in\sigma(X)$? b) Could you please elaborate on "it suffices to show.."? (It mostly confuses me as in the definition or $\sigma(X)$ we consider $\mathcal{S}$ as opposed to $\mathcal{S}_t$). c) What does the notation $(s_r)_{r \in T} $ mean? Sorry for being kinda slow, I have poor background in measure theory (working on that..)
Nov
9
revised Why does $\sigma (X_t) \subset \sigma (X)$ hold?
typo
Nov
9
asked Why does $\sigma (X_t) \subset \sigma (X)$ hold?
Oct
12
accepted Smallest $\sigma$-algebra and $\sigma$-algebra generated by a function