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Ergodic averages of commuting transformations with distinct degree polynomial iterates
We prove mean convergence, as N → ∞, for the multiple ergodic averages 1 N ∑ n = 1 N f 1 ( T 1 p 1 ( n ) x ) ⋅ … ⋅ f l ( T l p l x ) where p1, …, pℓ are integer …