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Tag Archives: ergodic theorem
Convergence and Recurrence of Z actions
Ergodic Ramsey Theory started with Furstenberg’s proof of Szemeredi’s theorem in arithmetic progressions in 1977. Through a correspondence principle, Furstenberg realized that Szemeredi’s theorem follows from a dynamical statement: for every invertible, ergodic measure preserving transformation of a probability space … Continue reading
Posted in Ergodic Theory, State of the art
Tagged Austin, Bergelson, convergence, Conze, ergodic theorem, Furstenberg, Host, Katznelson, Kra, Leibman, Lesigne, Poincare, recurrence, Tao, Walsh
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On {x+y,xy} patterns in large sets of countable fields
Vitaly Bergelson and I have recently uploaded to the arXiv our joint paper `On patterns in large sets of countable fields‘. We prove a result concerning certain monochromatic structures in countable fields and a corresponding density version. Schur’s Theorem, proved … Continue reading
The Ergodic Theorem
— 1. Introduction — One can argue that (modern) ergodic theory started with the ergodic Theorem in the early 30’s. Vaguely speaking the ergodic theorem asserts that in an ergodic dynamical system (essentially a system where “everything” moves around) the … Continue reading
Posted in Analysis, Classic results, Ergodic Theory, Tool
Tagged Akcoglu, Birkhoff, del Junco, ergodic theorem, Lindenstrauss, Rohlin, Rokhlin, von Neumann
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