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The integral of each such simple function

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Recall that the support of a function f : Rn â?'R is the closure of the

set {x É? Rn : f(x) = 0}. Prove that if f : Rnâ?' Rn has support in a

set of Lebesgue measure =0, then â?«Rn f(x)dx = 0.

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The integral of each such simple function is investigated.

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