×

Uniqueness of invariant means for measure-preserving transformations. (English) Zbl 0464.28008


MSC:

28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
28D15 General groups of measure-preserving transformations
43A07 Means on groups, semigroups, etc.; amenable groups
43A40 Character groups and dual objects

Citations:

Zbl 0425.43001
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] S. Banach, Sur le problème de la mesure, Oeuvres, Vol. I, PWN, Warsaw, 1967, pp. 318-322.
[2] Andrés del Junco and Joseph Rosenblatt, Counterexamples in ergodic theory and number theory, Math. Ann. 245 (1979), no. 3, 185 – 197. · Zbl 0398.28021 · doi:10.1007/BF01673506
[3] Edmond Granirer, Criteria for compactness and for discreteness of locally compact amenable groups, Proc. Amer. Math. Soc. 40 (1973), 615 – 624. · Zbl 0274.22009
[4] Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. · Zbl 0174.19001
[5] V. Losert and H. Rindler, Almost invariant sets, Bull. London Math. Soc. 13 (1981), no. 2, 145 – 148. · Zbl 0462.43002 · doi:10.1112/blms/13.2.145
[6] E. Marczewski (Szprilrajn), Problem \( 169\), The Scottish Book, 1937-1938.
[7] Jan Mycielski, Equations unsolvable in \?\?\(_{2}\)(\?) and related problems, Amer. Math. Monthly 85 (1978), no. 4, 263 – 265. · Zbl 0382.20036 · doi:10.2307/2321170
[8] Jan Mycielski, Finitely additive invariant measures. I, Colloq. Math. 42 (1979), 309 – 318. J. M. Rosenblatt, Finitely additive invariant measures. II, Colloq. Math. 42 (1979), 361 – 363. · Zbl 0431.28003
[9] Jan Mycielski, Finitely additive invariant measures. I, Colloq. Math. 42 (1979), 309 – 318. J. M. Rosenblatt, Finitely additive invariant measures. II, Colloq. Math. 42 (1979), 361 – 363. · Zbl 0431.28003
[10] I. Namioka, Følner’s conditions for amenable semi-groups, Math. Scand. 15 (1964), 18 – 28. · Zbl 0138.38001 · doi:10.7146/math.scand.a-10723
[11] Jan Mycielski, Finitely additive invariant measures. I, Colloq. Math. 42 (1979), 309 – 318. J. M. Rosenblatt, Finitely additive invariant measures. II, Colloq. Math. 42 (1979), 361 – 363. · Zbl 0431.28003
[12] Joseph Max Rosenblatt, Invariant means for the bounded measurable functions on a non-discrete locally compact group, Math. Ann. 220 (1976), no. 3, 219 – 228. · Zbl 0305.43002 · doi:10.1007/BF01431093
[13] Walter Rudin, Invariant means on \?^{\infty }, Studia Math. 44 (1972), 219 – 227. Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity, III. · Zbl 0238.43002
[14] K. Schmidt, Asymptotically invariant sequences and an action of \( SL(2,Z)\) on the \( 2\)-sphere (preprint). · Zbl 0485.28018
[15] -, Amenability, Kazhdan’s property \( T\), strong ergodicity, and invariant means for ergodic actions (preprint).
[16] Dennis Sullivan, For \?>3 there is only one finitely additive rotationally invariant measure on the \?-sphere defined on all Lebesgue measurable subsets, Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 1, 121 – 123. · Zbl 0459.28009
[17] Stanton M. Trott, A pair of generators for the unimodular group, Canad. Math. Bull. 5 (1962), 245 – 252. · Zbl 0107.02503 · doi:10.4153/CMB-1962-024-x
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.