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Jul 22, 2013 at 1:21 comment added Noah Stein @KeivanKarai: I believe in that case you can get a counterexample by letting $X(\omega) = 2\omega \mod 1$ and $Y(\omega) = 3\omega\mod 1$, though I haven't checked the details.
Jul 19, 2013 at 23:13 vote accept Keivan Karai
Jul 19, 2013 at 23:10 comment added Keivan Karai Thank you. What if if I do not insist on $T$ being invertible?
Jul 19, 2013 at 22:40 history answered Noah Stein CC BY-SA 3.0