# 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

## 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