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Is there any example of a function $f(x,y):[0,1]$x$[0,1]\to \mathbb R$ so that $\int_{0}^1\int_{0}^1f(x,y)dydx$ and $\int_{0}^1\int_{0}^1f(x,y)dxdy$ exists and are equal but $\int\int f(x,y)dydx$ does not exists in $[0,1]$x$[0,1]$?

I´ve been trying to find and example but i have nothing so far; I would really appreciate if yo can help me with this problem

Counterexamples in Double Integral in this link they talk about a non integrable function (sierpinski) that has this properties but Is there an easier example?

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