Using the definition of conditional expectation using the projection, show that for any variables Y1,...,Yk, ZE L2(12, F,P()) and any (measurable) function h : Rk → R, E[Zh(Y1, ...,Yk) |Y1, ...,Yk] = E(Z |Y1, ... ,Yk]h(Y1,...,Yk). , , [ ( This is called the product rule for conditional expectation.
