- #1
Kevin_spencer2
- 29
- 0
Hello, my question is how could we define integration on infinite dimensional spaces?, my idea is, let be the multiple integral.
[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?
[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?