276 citations · 4.5k across the 293 of their papers we have counts for
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Measurable tilings by abelian group actions
Jan Grebík, Rachel Greenfeld, Václav Rozhoň +1
Let be a measure space with a measure-preserving action of an abelian group . We consider the problem of understanding the structure of measurable…
The structure of arbitrary Conze-Lesigne systems
Asgar Jamneshan, Or Shalom, Terence Tao
Let be a countable abelian group. An (abstract) -system - that is, an (abstract) probability space equipped with an (abstract) probability-preserving action of…
An uncountable Mackey-Zimmer theorem
Asgar Jamneshan, Terence Tao
The Mackey-Zimmer theorem classifies ergodic group extensions of a measure-preserving system by a compact group , by showing that such extensions are isomorphic to a gro…
Pointwise ergodic theorems for non-conventional bilinear polynomial averages
Ben Krause, Mariusz Mirek, Terence Tao
We establish convergence in norm and pointwise almost everywhere for the non-conventional (in the sense of Furstenberg) bilinear polynomial ergodic averages \[ A_N(f,g)(x) := \frac…
An uncountable Moore-Schmidt theorem
Asgar Jamneshan, Terence Tao
We prove an extension of the Moore-Schmidt theorem on the triviality of the first cohomology class of cocycles for the action of an arbitrary discrete group on an arbitrary measure…
Failure of the pointwise and maximal ergodic theorems for the free group
Terence Tao
Let denote the free group on two generators . For any measure-preserving system on a finite measure space $X = (X,{\mathcal X},…