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On transformations without finite invariant measure. (English) Zbl 0286.28017

MSC:
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
28D05 Measure-preserving transformations
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[1] Calderon, A., Sur LES mesures invariantes, C. R. acad. sci. Paris, 240, 1960-1962, (1955) · Zbl 0064.05102
[2] Dowker, Y.N., On measurable transformations in finite measure spaces, Ann. of math., 62, 2, 504-516, (1955) · Zbl 0065.28701
[3] Dowker, Y.N., Sur LES applications measurables, C. R. acad. sci. Paris, 242, 329-331, (1956) · Zbl 0073.04002
[4] Dunford, N.; Schwartz, J.T., Linear operators I, (1958), Interscience
[5] Hajian, A.B., On ergodic measure preserving transformations defined on an infinite measure space, (), 45-48 · Zbl 0136.03703
[6] Hajian, A.B.; Ito, Y.; Kakatani, S., Invariant measures and orbits of dissipative transformations, Advances in math, 9, 52-65, (1972) · Zbl 0236.28010
[7] Hajian, A.B.; Kakutani, S., Weakly wandering sets and invariant measures, Trans. amer. math. soc., 110, 136-151, (1964) · Zbl 0122.29804
[8] Hajian, A.B.; Kakutani, S., Example of an ergodic measure preserving transformation on an infinite measure space, Springer lecture notes, 160, 45-52, (1970) · Zbl 0213.07601
[9] \scA. B. Hajian and S. Kakutani, Transformations of α-type, unpublished, proofs in [20]. · Zbl 0213.07601
[10] Helmberg, G.; Simons, F.H., Aperiodic transformations, Z. wahrscheinlichkeitstheorie verw. gebiete, 13, 180-190, (1969) · Zbl 0176.33902
[11] Hopf, E., Theory of measures and invariant integrals, Trans. amer. math. soc., 34, 373-393, (1932) · JFM 58.0250.02
[12] Jones, L.K., A Mean ergodic theorem for weakly mixing operators, Advan. math., 7, 211-216, (1971) · Zbl 0221.47007
[13] Krengel, U., Entropy of conservative transformations, Z. wahrscheinlichkeitstheorie verw. gebiete, 7, 161-181, (1967) · Zbl 0183.19303
[14] Krengel, U., Classification of states for operators, Proc. fifth Berkeley symp. math. stat. and prob., 1965, 2, 2, 415-429, (1967)
[15] Krengel, U., Transformations without finite invariant measure have finite strong generators, Springer lecture notes, 160, 133-157, (1970) · Zbl 0201.38303
[16] Krengel, U., Recent results on generators in ergodic theory, (), 465-482
[17] Neveu, J., Existence of bounded invariant measures in ergodic theory, Proc. fifth Berkeley symp. math. stat. and prob., 1965, 2, 2, 461-472, (1967)
[18] Ornstein, D., The sums of iterates of a positive operator, (), 85-115
[19] Sucheston, L., On existence of finite invariant measures, Math. Z., 86, 327-336, (1964) · Zbl 0128.11404
[20] Osikawa, M.; Hamachi, T., On zero type and positive type transformations with infinite invariant measure, Mem. fac. sci. kyushu univ. ser. A, math., 25, 280-295, (1971) · Zbl 0224.28013
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