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4h
comment Independence between conditional expectations
Thanks. how do you determine E[X∣X+Y]?
5h
comment What can be said about $E(X|N)$ when $N \subset \sigma(X) $?
yes, N is a σ-algebra
5h
asked What can be said about $E(X|N)$ when $N \subset \sigma(X) $?
6h
accepted Are the converses of the following special cases of conditional expectation also true?
6h
reviewed Reject and Edit Determine measurability of E(X|N) or even $\sigma(E(X|N))$?
6h
revised Determine measurability of E(X|N) or even $\sigma(E(X|N))$?
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6h
comment Determine measurability of E(X|N) or even $\sigma(E(X|N))$?
Are σ(E(X|N)) and σ(σ(X)∩N) equal, or is one a subset of the other?
6h
comment Determine measurability of E(X|N) or even $\sigma(E(X|N))$?
Thanks. How do you determine E(X|N)? Some general rule?
6h
comment Determine measurability of E(X|N) or even $\sigma(E(X|N))$?
how do you determine σ(E(X|N))? Are σ(E(X|N)) and σ(σ(X)∩N) equal, or one is the subset of the other?
6h
comment Independence between conditional expectations
Is there relation between $\sigma(E(X|N))$ and $\sigma(\sigma(X) \cap N)$? math.stackexchange.com/questions/1420189/…
6h
revised Determine measurability of E(X|N) or even $\sigma(E(X|N))$?
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7h
asked Determine measurability of E(X|N) or even $\sigma(E(X|N))$?
7h
comment Independence between conditional expectations
right. @Domink. thanks. How about the second question? I was wondering if E(X|N) must be measurable wrt both sigma(X) and N?
8h
asked Independence between conditional expectations
9h
comment Are the converses of the following special cases of conditional expectation also true?
why "both X and Y are square-integrable"?
11h
comment Are the converses of the following special cases of conditional expectation also true?
Thanks. what is about X that is equivalent to E(X|N)=EX a.e., if independence is too much?
12h
asked Are the converses of the following special cases of conditional expectation also true?
2d
comment Is conditional expectation E(X|N) an a.e. equivalence class wrt N or underlying sigma algebra?
Let me put it in another way: If Y1 and Y2 are both in E(Y|N), are they equal a.e. (wrt N)?
2d
comment Is conditional expectation E(X|N) an a.e. equivalence class wrt N or underlying sigma algebra?
"It's conceivable that you can specify criterion to partition E(X|N) into disjoint classes" doesn't make sense. I guess you know that the a.e. is a equivalent relation on the set of random variables, so the a.e. relation partitions the set of r.v.s. into equivalent classes. it isn't what I can change. My last comment is a well defined question
2d
comment Is conditional expectation E(X|N) an a.e. equivalence class wrt N or underlying sigma algebra?
In that new measure space, can E(X|N) be several a.e. equivalent classes of N measurable functions?