| Abstract |
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We will review recent advances in nonuniform measure rigidity for abelian
actions. In particular nonlinear actions on the torus and general
nonuniformly hyperbolic actions. One of the main examples of measure
rigidity is x2 x3 Furstenberg unsolved problem stating that the unique
invariant measure without atoms is Lebesgue. We shall discuss nonlinear
versions of such problems.
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