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[tex] \int_{V}dVf(X) [/tex] where [tex] X=(x_1 ,x_2 , x_3 ,.....,x_n ) [/tex]

then i define a family of trial functions, in my case they are just 'step functions' so [tex] H(X)=H(x_1) H(x_2 ) H(x_3 ).....H(x_n) [/tex] and define a some kind of axiomatic integral for htem (i don't know how unfortunately) then i try to apply integration by parts so integral hold to and make n -> infinite so we define an infinite dimensional integral.

By the way, is there an analogue to Euler-Mc Laurin sum formula for infinite dimensional spaces?