Mixing
![English Logic Puzzle [closed]](https://lh5.googleusercontent.com/-ffWFm9uJgO4/AAAAAAAAAAI/AAAAAAAABjI/hXd8V3yjdoE/s72-c/photo.jpg?sz=32)
Proof that $E(X|sigma (G_1,G_2))=E(X|G_1)$, when $G_2,sigma(sigma(X),G_1)$ independent.
I want to prove:
$$E(X|sigma (G_1,G_2))=E(X|G_1)$$
when $G_2,sigma(sigma(X),G_1)$ are independent. It's quite elusive expression to unpack, what would you say is the meaning? Previously I have proven that:
$L={Ain F| E(I_AX)=E(I_AE(X|G_1)}$ is a $lambda$-system and contains the set: ${ Acap B| Ain G_1,Bin G_2}$. Note that $F$ is the simga algebra of the space which $G_1,G_2$ are subsets of.
How to continue from here?
measure-theory
asked Nov 20 '18 at 2:45
Dole
906514
add a comment |
I want to prove:
$$E(X|sigma (G_1,G_2))=E(X|G_1)$$
when $G_2,sigma(sigma(X),G_1)$ are independent. It's quite elusive expression to unpack, what would you say is the meaning? Previously I have proven that:
$L={Ain F| E(I_AX)=E(I_AE(X|G_1)}$ is a $lambda$-system and contains the set: ${ Acap B| Ain G_1,Bin G_2}$. Note that $F$ is the simga algebra of the space which $G_1,G_2$ are subsets of.
How to continue from here?
measure-theory
asked Nov 20 '18 at 2:45
Dole
906514
2
math.stackexchange.com/questions/365310/…
– d.k.o.
Nov 20 '18 at 4:21
add a comment |
I want to prove:
$$E(X|sigma (G_1,G_2))=E(X|G_1)$$
when $G_2,sigma(sigma(X),G_1)$ are independent. It's quite elusive expression to unpack, what would you say is the meaning? Previously I have proven that:
$L={Ain F| E(I_AX)=E(I_AE(X|G_1)}$ is a $lambda$-system and contains the set: ${ Acap B| Ain G_1,Bin G_2}$. Note that $F$ is the simga algebra of the space which $G_1,G_2$ are subsets of.
How to continue from here?
measure-theory
asked Nov 20 '18 at 2:45
Dole
906514
I want to prove:
$$E(X|sigma (G_1,G_2))=E(X|G_1)$$
when $G_2,sigma(sigma(X),G_1)$ are independent. It's quite elusive expression to unpack, what would you say is the meaning? Previously I have proven that:
$L={Ain F| E(I_AX)=E(I_AE(X|G_1)}$ is a $lambda$-system and contains the set: ${ Acap B| Ain G_1,Bin G_2}$. Note that $F$ is the simga algebra of the space which $G_1,G_2$ are subsets of.
How to continue from here?
measure-theory
measure-theory
asked Nov 20 '18 at 2:45
Dole
906514
asked Nov 20 '18 at 2:45
Dole
906514
asked Nov 20 '18 at 2:45
Dole
906514
asked Nov 20 '18 at 2:45
Dole
906514
asked Nov 20 '18 at 2:45
Dole
906514
906514
2
math.stackexchange.com/questions/365310/…
– d.k.o.
Nov 20 '18 at 4:21
add a comment |
2
math.stackexchange.com/questions/365310/…
– d.k.o.
Nov 20 '18 at 4:21
2
2
math.stackexchange.com/questions/365310/…
– d.k.o.
Nov 20 '18 at 4:21
math.stackexchange.com/questions/365310/…
– d.k.o.
Nov 20 '18 at 4:21
add a comment |
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math.stackexchange.com/questions/365310/…
– d.k.o.
Nov 20 '18 at 4:21