Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions

H. Furstenberg,The structure of distal flows, Amer. J. Math.85 (1963), 477–515.

A. Y. Khintchine,Three Pearls of Number Theory, Graylock Press, New York, 1952.

U. Krengel,Weakly wandering vectors and weakly independent partitions, Trans. Amer. Math. Soc.164 (1972), 199–226.

G. W. Mackey,Induced representation of locally compact groups, I, Ann. of Math.55 (1952), 101–139.

K. F. Roth,Sur quelques ensembles d'entiers, C. R. Acad. Sci. Paris234 (1952), 388–390.

E. Szemerédi,On acts of integers containing no four elements in arithmetic progression, Acta Math. Acad. Sci. Hungar.20 (1969), 89–104.

E. Szemerédi,On acts of integers containing no k elements in arithmetic progression, Acta Arith.27 (1975), 199.

R. Zimmer,Ergodic actions with generalized discrete spectrum, to appear.