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If we have $E(x|y)=E(x|z)=0$, does it follow that $E(x|y,z)=0$?

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  • $\begingroup$ Your second conditional expectation specified no value. Please check my edit. $\endgroup$ – Christoph Hanck Jan 18 '18 at 9:49
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No. Let $E[z|y] = -y$, $E[y|z]= -z$ and $x = y +z$. Then $E[x|y] = y + E[z|y] = y -y = 0$, $E[x|z] = E[y|z] + z = -z + z = 0$ but $E[x|y,z] = y + z$.

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