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Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions. (English) Zbl 0347.28016


MSC:

28D05 Measure-preserving transformations
47A35 Ergodic theory of linear operators
54H20 Topological dynamics (MSC2010)
11B83 Special sequences and polynomials
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References:

[1] Furstenberg, H., The structure of distal flows, Amer. J. Math., 85, 477-515 (1963) · Zbl 0199.27202 · doi:10.2307/2373137
[2] Khintchine, A. Y., Three Pearls of Number Theory (1952), New York: Graylock Press, New York · Zbl 0048.27202
[3] Krengel, U., Weakly wandering vectors and weakly independent partitions, Trans. Amer. Math. Soc., 164, 199-226 (1972) · Zbl 0205.13903 · doi:10.2307/1995969
[4] Mackey, G. W., Induced representation of locally compact groups, I, Ann. of Math., 55, 101-139 (1952) · Zbl 0046.11601 · doi:10.2307/1969423
[5] Roth, K. F., Sur quelques ensembles d’entiers, C. R. Acad. Sci. Paris, 234, 388-390 (1952) · Zbl 0046.04302
[6] Szemerédi, E., On acts of integers containing no four elements in arithmetic progression, Acta Math. Acad. Sci. Hungar., 20, 89-104 (1969) · Zbl 0175.04301 · doi:10.1007/BF01894569
[7] Szemerédi, E., On acts of integers containing no k elements in arithmetic progression, Acta Arith., 27, 199-199 (1975) · Zbl 0303.10056
[8] R. Zimmer,Ergodic actions with generalized discrete spectrum, to appear. · Zbl 0349.28011
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