The ergodic theoretical proof of Szemerédi's theorem
暂无分享,去创建一个
Partial results were obtained previously by K. F. Roth (1952) who established the existence of arithmetic progressions of length three in subsets of Z of positive upper density, and by E. Szemeredi (1969) who proved the existence of progressions of length four. In 1976 Furstenberg noticed that the statement of Theorem I is equivalent to a statement about "multiple recurrence" of measure-preserving transformations, namely
[1] P. Halmos. Lectures on ergodic theory , 1956 .
[2] H. Furstenberg,et al. An ergodic Szemerédi theorem for commuting transformations , 1978 .