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integral over difference of sets
Posted:
Nov 8, 2010 1:37 PM


Hello everyone, I know that the integral of a simple function over the sum of two sets is the integral of the function over each individual set. (Additivity for simple functions). My question is if B is a subset of A. Is the integral over the difference (AB) the difference of the integrals, i.e the difference of the integtral of the function over A minus the integral of the function over B.
To put it another way does sum(ai* x m{x in AB yi1<=f(x)<yi})=sum(ai* x m{x in A yi1<=f(x)<yi}sum(ai* x m{x in B yi1<=f(x)<yi})?
I know this is simply a matter of set logic but it has me confused. If someone can explain I would appreciate it very much.



