content_image/319128.jpg content_image/319126.jpg content_image/319127.jpg
ψ ∈ D ( W ) by 

<img src='content_image/319128.jpg'>

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. 

<img src='content_image/319126.jpg'>

<img src='content_image/319127.jpg'>

