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invertible, measurable and measure preserving
$T: [0,1)^{2}\rightarrow[0,1)^{2}$ by
$T(x,y) = (2x,\frac{y}{2})$, with $0 \leq x < \frac{1}{2}$
and
$T(x,y) = (2x-1, \frac{y+1}{2})$, with $\frac{1}{2} \leq x < 1$
In class we said this $T$ ...
