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Homework Statement
Show that
[tex] \int_{A} 1 = \int_{T(A)} 1 [/tex]
given A is an arbitrary region in R^n (not necessarily a rectangle) and T is a translation in R^n.
Homework Equations
Normally we find Riemann integrals by creating a rectangle R that includes A and set the function to be zero when x is in R\A and x is in A. I can only use the definition.
The Attempt at a Solution
I tried to create a rectangle that includes both A and T(A). However that was not useful. I'm really at a lost here.
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