State the Fubini Theorem for the product of three σ-finite meas... | Filo
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Although Fubini's theorem holds for most functions met in practice, we must still exercise some caution. This exercise gives a function for which it fails. By using a substitution involving the tangent function, show that ∫0^1 ∫0^1 (x^2-y^2)/((x^2 y^2)^2) d y d x=(π)/(4) yet ∫0^1 d^(x^2-y^2)/(1-x^2-1) d x=-(x^2)/(4) 2 x 4=(7)/(4) d x Why does this not contradict Theorem 3 or 3^'' ? | Numerade
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