Denote by (lambda) Lebesgue measure on ((-1,1)). Show that the iterated integrals exist and coincide, [int_{(-1,1)} int_{(-1,1)}
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Denote by \(\lambda\) Lebesgue measure on \((-1,1)\). Show that the iterated integrals exist and coincide,
\[\int_{(-1,1)} \int_{(-1,1)} \frac{x y}{\left(x^{2}+y^{2}ight)^{2}} \lambda(d x) \lambda(d y)=\int_{(-1,1)} \int_{(-1,1)} \frac{x y}{\left(x^{2}+y^{2}ight)^{2}} \lambda(d y) \lambda(d x)\]
but that the double integral does not exist.
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