= An antisymmetric kernel with unequal iterated integrals
{title2=$f(x,y)=\frac{x-y}{(x+y)^3}$}
The function $(x-y)/(x+y)^3$ on the <unit square> is not <Lebesgue integrable>. On $0<y<x/2$, its absolute value is at least $4/(27x^2)$, whose <area> <integral> diverges logarithmically. Its two signed <iterated integrals> nevertheless exist, ignoring null boundary sections, and equal $1/2$ and $-1/2$. This illustrates why <absolute integrability> is required for <Fubini's theorem>.
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