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 Mar15 comment simple conditional expectation @Did Since $\eta$ is not discrete here, I would use: $Z:=E[\xi|\eta]$ is the r.v. so that $Z$ is $\sigma(\eta)$ measurable and for every $A\in\sigma(\eta)$ we have $E[Z\mathbf1_A] = E[\xi\mathbf1_A]$ (I omit the integrability condition). If there is an easier way, I'm happy to hear that one. Mar15 comment simple conditional expectation Thanks for the quick response. Could you explain how you got the answer? Mar15 revised simple conditional expectation added 116 characters in body Mar15 comment simple conditional expectation I have the example from a book, see edited post. The claim the solution is $E[\xi|eta](x)=\frac{1}{6}\mathbf1_{x\in[0,\frac{1}{2})}+2x^2\mathbf1_{x\in [ \frac{1}{2},2]}$ Mar15 asked simple conditional expectation Feb12 accepted Solving equation with two equations for one paramter using constraints Feb9 asked Solving equation with two equations for one paramter using constraints Dec27 asked Is this really a solution to the PDE? Dec8 awarded Caucus Dec4 awarded Yearling Nov24 comment Stopping Time Subset Proof I'm wonder why my asnwer was downvoted. I would appreciate a feedback on this. Nov24 comment Stopping Time Subset Proof @Did obviously, that was a typo. Nov24 revised Stopping Time Subset Proof edited body Nov24 answered Stopping Time Subset Proof Nov7 accepted How correctly apply a Taylor expansion of first order to a multivariate function decomposition. Nov7 revised How correctly apply a Taylor expansion of first order to a multivariate function decomposition. deleted 68 characters in body Nov7 revised How correctly apply a Taylor expansion of first order to a multivariate function decomposition. deleted 68 characters in body Nov7 asked How correctly apply a Taylor expansion of first order to a multivariate function decomposition. Aug18 asked Solving optimization problem over time Mar21 awarded Benefactor