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Oct 31, 2019 at 11:08 comment added minimore99 Sorry I should have made it clearer: I don't know if $f$ is injective or not, but from @e.lipnowski comments it seems that $f$ isn't injective even if it's 1-Lipschitz, in which case I should suppose the MI is not preserved?
Oct 31, 2019 at 10:39 comment added e.lipnowski Whoops! Thank you and sorry.
Oct 31, 2019 at 3:17 comment added Yuval Peres Note the OP assumed $f$ is injective
Oct 31, 2019 at 0:41 history answered e.lipnowski CC BY-SA 4.0