Some effective results for ×a×b

Jean Bourgain*, Elon Lindenstrauss, Philippe Michel, Akshay Venkatesh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We provide effective versions of theorems of Furstenberg and RudolphJohnson regarding closed subsets and probability measures of ℝ/ℤ invariant under the action of a non-lacunary multiplicative semigroup of integers. In particular, we give an explicit rate at which the sequence {anb kx}n,k becomes dense for a,b fixed multiplicatively independent integers and x∈ℝ/ℤ Diophantine generic.

Original languageAmerican English
Pages (from-to)1705-1722
Number of pages18
JournalErgodic Theory and Dynamical Systems
Issue number6
StatePublished - Dec 2009


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