Invariant measures and the set of exceptions to Littlewood ’ s conjecture

  title={Invariant measures and the set of exceptions to Littlewood ’ s conjecture},
  author={Manfred Einsiedler and Anatole Katok and Elon Lindenstrauss},
We classify the measures on SL(k,R)/SL(k,Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set of exceptions to Littlewood’s conjecture has Hausdorff dimension zero. 

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