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References
J. AARONSON: On the Categories of Ergodicity when the Measure is Infinite. Ergodic Theory, Proceedings Oberwolfach 1978, Springer Lecture Notes in Math 729 (1979), 1–7.
J. AARONSON: The Asymptotic Distributional Behaviour of Transformations Preserving Infinite Measures. J. d'analyse 39 (1981), 203–234.
S. ALPERN: New Proofs that Weak Mixing is Generic. Inventiones Math. 32 (1976), 263–278.
S. ALPERN: Approximation to and by Measure Preserving Homeomorphisms. J. London Math. Soc. 18 (1978), 305–315.
S. ALPERN: A Topological Analog of Halmos' Conjugacy Lemma. Inventiones Math. 48 (1978), 1–6.
S. ALPERN: Generic Properties of Measure Preserving Homeomorphisms. Ergodic Theory, Proceedings Oberwolfach 1978, Springer Lecture Notes in Math. 729 (1979), 16–27.
S. ALPERN: Measure Preserving Homeomorphisms of ℝn. Indiana U. Math. J. 28 (1979), 957–960.
S. ALPERN: Return Times and Conjugates of an Antiperiodic Transformation. Ergodic Theory & Dynamical Systems, 1 (1981), 135–143.
S. ALPERN: Nonstable Ergodic Homeomorphisms of ℝ4, Indiana U. Math. J. 32 (1983), 187–191.
S. ALPERN & R. D. EDWARDS: Lusin's Theorem for Measure Preserving Homeomorphisms. Mathematika 26 (1979), 33–43.
J. R. BROWN: Approximation Theorems for Markov Operators. Pacific J. Math. 16 (1966), 13–23.
R. V. CHACON: Approximation of Transformations with Continuous Spectrum. Pacific J. Math. 31 (1969), 293–302.
R. V. CHACON: Weakly Mixing Transformations which are not Strongly Mixing. Proc. Amer. Math. Soc. 22 (1969), 559–562.
R. V. CHACON AND N. A. FRIEDMAN: Approximation and Invariant Measures. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1965), 286–295.
J. R. CHOKSI, J. HAWKINS & V. S. PRASAD: Type III1 Transformations and their Cocycle Extensions. (to appear).
J. R. CHOKSI & S. KAKUTANI: Residuality of Ergodic Measurable Transformations and of Ergodic Transformations which Preserve an Infinite Measure. Indiana U. Math. J. 28 (1979), 453–469.
J. R. CHOKSI & V. S. PRASAD: Ergodic Theory on Homogeneous Measure Algebras. Measure Theory Oberwolfach 1981, Proceedings, Springer Lecture Notes in Math. 945 (1982), 366–408.
N. A. FRIEDMAN: Introduction to Ergodic Theory, Van Nostrand Reinhold Studies in Math. No. 29, New York, 1970.
P. R. HALMOS: Measure Theory. D. Van Nostrand, New York 1950; reprinted Springer, New York, 1975.
P.R. HALMOS: Lectures on Ergodic Theory. Publ. Math. Soc. Japan, Tokyo 1956; reprinted Chelsea, New York 1960.
P. R. HALMOS: Approximation Theories for Measure Preserving Transformations. Trans. Amer. Math. Soc. 55 (1944), 1–18.
P. R. HALMOS: In General a Measure Preserving Transformation is Mixing. Ann. of Math. 45 (1944), 786–792.
A. IONESCU TULCEA: On the Category of Certain Classes of Transformations in Ergodic Theory. Trans. Amer. Math. Soc. 114 (1965), 261–279.
A. IWANIK: Approximation Theorems for Stochastic Operators. Indiana U. Math. J. 29 (1980), 415–425.
A. DEL JUNCO: Disjointness of Measure Preserving Transformations, Minimal Self-Joinings and Category. Ergodic Theory and Dynamical Systems I, Proceedings Special Year, Maryland 1979–80, Progress in Math. 10, Birkhauser, Boston, 1981, 81–89.
S. KAKUTANI: Induced Measure Preserving Transformations. Proc. Imperial Acad. Tokyo 19 (1943), 635–641.
S. KAKUTANI & W. PARRY: Infinite Measure Preserving Transformations with "Mixing". Bull. Amer. Math. Soc 69 (1963), 752–756.
A.B. KATOK & E.A. ROBINSON: Constructions in Ergodic Theory. (To appear).
A. B. KATOK & A.M. STEPIN: Approximations in Ergodic Theory (Russian). Uspekhi Math. Nauk 22 (1967), 81–106; translated in Russian Math. Surveys 22 (1967), 77–102.
A. B. KATOK & A. M. STEPIN: Metric Properties of Measure Preserving Homeomorphisms (Russian). Uspekhi Math. Nauk 25 (1970), 193–220; translated in Russian Math. Surveys 25 (1970), 191–220.
U. KRENGEL: Entropy of Conservative Transformations. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 7 (1966), 161–181.
U. KRENGEL & L. SUCHESTON: On Mixing in Infinite Measure Spaces. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 13 (1969), 150–164.
K. KRICKEBERG: Mischende Transformationen auf Mannigfaltigkeiten Unendlichen Masses. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 7 (1967), 235–247.
J. C. OXTOBY: Approximation by Measure Preserving Homeomorphisms. Recent Advances in Topological Dynamics, Proc. of Conf. in honour of G. A. Hedlund at Yale U. June 1972, Springer, Lecture Notes in Math. 318 (1973), 206–217.
J. C. OXTOBY & V. S. PRASAD: Homeomorphic Measures in the Hilbert Cube. Pacific J. Math. 77 (1978), 483–497.
J. C. OXTOBY & S. M. ULAM: Measure Preserving Homeomorphisms and Metrical Transitivity. Ann. of Math. 42 (1941), 874–920.
V. S. PRASAD: Ergodic Measure Preserving Homeomorphisms of Rn, Indiana U. Math. J. 28 (1979), 859–867.
V. S. PRASAD: A Mapping Theorem for Hilbert Cube Manifolds. Proc. Amer. Math. Soc. (to appear).
V. S. PRASAD: Generating Dense Subgroups of Measure Preserving Transformations. Proc. Amer. Math. Soc. 83 (1981), 286–288.
V. S. PRASAD: Sous-groupes libres et sous-ensembles indépendants, de transformations préservant la mesure. Proceedings of the Workshop on Measure Theory and its Applications (Sherbrooke, 1982), Lecture Notes in Mathematics, Springer-Verlag.
V. A. ROHLIN: A General Measure Preserving Transformation is not Mixing (Russian). Doklady Akad. Nauk S.S.S.R. (N.S.) 60 (1948), 349–351.
V. A. ROHLIN: Selected Problems in the Metric Theory of Dynamical Systems (Russian). Uspekhi Math. Nauk, 30 (1949), 57–128; translated in Amer. Math. Soc. Translations (2) 49 (1966), 171–240.
V. A. ROHLIN: Entropy of Metric Endomorphisms (Russian). Doklady Akad. Nauk S.S.S.R. (N.S.) 124 (1959), 980–983.
U. SACHDEVA: On Category of Mixing in Infinite Measure Spaces. Math. Systems Theory 5 (1971), 319–330.
H. E. WHITE Jr.: The Approximation of one-one Measurable Transformations by Measure Preserving Homeomorphisms. Proc. Amer. Math. Soc. 44 (1974), 391–394.
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Choksi, J.R., Prasad, V.S. (1983). Approximation and baire category theorems in ergodic theory. In: Belley, JM., Dubois, J., Morales, P. (eds) Measure Theory and its Applications. Lecture Notes in Mathematics, vol 1033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099849
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