Then Σ$_{v}$ ∫ g ( y ) f$_{y}$$_{|}$$_{x}$ ( x, y ) ψ$_{v}$ ( y ) dy = ∫ g ( y ) f$_{y}$$_{|}$$_{x}$ ( x, y )Σ$_{v}$ ψ$_{v}$ ( y ) dy = g ( y ) f$_{y}$$_{|}$$_{x}$ ( x, y ) dy, 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}$ ) = Then the conditional moment m as a generalized function on D ( W ) is given by ( m, ψ ) = with any { ψ$_{v}$ } representing a partition of unity on R d$_{y}$ by functions from D ( R d$_{y}$ ) . 28 Σ$_{v}$( − 1) d$_{x}$ + d$_{y}$ ∫ ... ∫ F$_{x,y}$ ( x, y ) ∂ $^{d$_{x}$}$ψ ( F$_{x}$ ( x )) ∂ $^{d$_{y}$}$[ g ( y ) ψ$_{v}$ ( y$_{1}$, ..., y$_{d}$$_{y}$ ) ] dF$_{x}$ ( x ) dy$_{1}$...dy$_{d}$$_{y}$ (21) ( − 1) d$_{x}$ + d$_{y}$ ∫ ... ∫ F$_{x,y}$ ( x, y ) ∂ $^{d$_{x}$}$ψ ( F$_{x}$ ( x )) ∂ $^{d$_{y}$}$[ g ( y ) ψ$_{v}$ ( y$_{1}$, ..., y$_{d}$$_{y}$ ) ] dF$_{x}$ ( x ) dy$_{1}$...dy$_{d}$$_{y}$. (20)