content_image/312432.jpg content_image/312439.jpg content_image/312438.jpg
Then 

<img src='content_image/312432.jpg'>

in other words interchanging the order of integration and summation is per- mitted for the terms on the left-hand side of (18) under Assumption 4. How- ever, this is not the case for terms on the right-hand side of (18) . For example, if g ( y ) = y, we have ∂ d$_{y}$ ( g ( y ) ψ$_{v}$ ( y )) = yψ ′ $_{v}$+ ψ$_{v}$, and Σ$_{v}$ ( ∂ d$_{y}$ ( g ( y ) ψ$_{v}$ ( y )) ) = 1 , but ∫ F$_{y}$$_{|}$$_{x}$ ( x, y ) dy may not exist. 

Thus ( gf$_{y}$$_{|}$$_{x}$, ψψ$_{ν}$ ) = 

<img src='content_image/312439.jpg'>

Then the conditional moment m as a generalized function on D ( W ) is given by ( m, ψ ) = 

<img src='content_image/312438.jpg'>

with any { ψ$_{v}$ } representing a partition of unity on R d$_{y}$ by functions from D ( R d$_{y}$ ) . 

