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May 2, 2014 at 15:37 comment added Algernon Sure! That's what I am suggesting how you could try to find: non-trivial solutions of $\mu(f)=0$ (non-trivial in the sense that $\pi(f)\neq 0$ for at least one other shift-invariant measure $\pi$).
May 2, 2014 at 14:42 comment added user39115 Thanks, but I m fixing the measure $\mu$ At the beginning.
May 1, 2014 at 13:48 history answered Algernon CC BY-SA 3.0