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

Manfred Einsiedler, Anatole Katok, Elon Lindenstrauss

Research output: Contribution to journalArticle

83 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)513-560
Number of pages48
JournalAnnals of Mathematics
Volume164
Issue number2
DOIs
StatePublished - Sep 2006

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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