ψ ∈ D ( W ) by Because the supports of ψ$_{v}$ and of ψ are bounded and the function being integrated is bounded, the integral exists. Assumption 4. (Existence of conditional moment). For a partition of unity, { ψ$_{ν}$ } , the sum converges. Then (19) represents ( m ( x ) , ψ ) for the generalized function, m ( x ) = Σ$_{v}$ ∫ g ( y ) f$_{y}$$_{|}$$_{x}$ ( x, y ) ψ$_{v}$ ( y ) dy, on D ( W ) . Thus where the sum converges. 27 m ( x ) = ∫ g ( y ) f$_{y}$$_{|}$$_{x}$ ( x, y ) dy = Σ$_{v}$ ( gf$_{y}$$_{|}$$_{x}$, ψ$_{ν}$ ) , Σ$_{v}$( ∫ g ( y ) f$_{y}$$_{|}$$_{x}$ ( x, y ) ψ$_{v}$ ( y ) dy, ψ ) (19) ( ∫ g ( y ) f$_{y}$$_{|}$$_{x}$ ( x, y ) ψ$_{v}$ ( y ) dy, ψ ) = ( − 1) d$_{y}$ ∫ ∫ F$_{y}$$_{|}$$_{x}$ ( x, y ) ∂ d$_{y}$ ( g ( y ) ψ$_{v}$ ( y )) dyψ ( F ( x )) dF ( x ) = ( − 1) d$_{y}$ + d$_{x}$ ∫ F$_{x,y}$ ( x, y ) ∂ d$_{y}$ ( g ( y ) ψ$_{v}$ ( y )) dy ( ∂ $^{d$_{x}$}$ψ )( F ( x )) dF ( x ) .