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Topic: integral over difference of sets
Replies: 4   Last Post: Jul 3, 2013 12:21 PM

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integral over difference of sets
Posted: Nov 8, 2010 1:37 PM
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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 (A-B) 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 A-B|
yi-1<=f(x)<yi})=sum(ai* x m{x in A| yi-1<=f(x)<yi}-sum(ai* x m{x in
B| yi-1<=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.

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