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Approximation for the measures of ergodic transformations of the real line. (English) Zbl 0476.28010


MSC:

28D05 Measure-preserving transformations
37A99 Ergodic theory

Citations:

Zbl 0298.28015
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Full Text: DOI

References:

[1] Bugiel, P.: On the exactness of a class of endomorphisms of the real line. Zeszyty Nauk. Uniw. Jagielloń. Prace Math. [To appear ] · Zbl 0622.28013
[2] Doob, J. L., Stochastic processes (1953), New York: Wiley, New York · Zbl 0053.26802
[3] Jabloński, M., Lasota, A.: Absolutely continuous invariant measures for transformations on the real line. Zeszyty Nauk. Uniw. Jagielloń. Prace Math. [To appear ] · Zbl 0479.28013
[4] Kemperman, J. H.B., The ergodic behavior of a class of real transformations, Proceeding of the summer Res. Inst. on Statist. Inference for Sochastic Processes, Indiana Univ., Bloomington, Indiana 1974, 249-258 (1975), New York: Academic Press, New York · Zbl 0347.28015
[5] Kemperman, J.H.B.: The ergodic behavior of a class of real transformations. [Preprint] · Zbl 0347.28015
[6] Lasota, A.; Yorke, J. A., On the existence of invariant measures for piecewise monotonic transformations, Trans. Amer. Math. Soc., 186, 481-488 (1973) · Zbl 0298.28015
[7] Li, T. Y., Finite approximation for the Frobenius-Perron operator. A solution to Ulam’s conjecture, J. Approximation Theory, 17, 177-186 (1976) · Zbl 0357.41011
[8] Li, T. Y.; Yorke, J. A., Ergodic transformations from an interval into itself, Trans. Amer. Math. Soc., 235, 183-192 (1978) · Zbl 0371.28017
[9] Ratner, M., Bernoulli flows over maps of the interval, Israel J. Math., 31, 298-314 (1978) · Zbl 0435.58022
[10] Rechard, O., Invariant measures for many-one transformations, Duke-Math. J., 23, 477-488 (1956) · Zbl 0070.28001
[11] Schweiger, F., tanx is ergodic, Proc. Amer. Math. Soc., 1, 54-56 (1978) · Zbl 0361.28011
[12] Ulam, S. M., A collection of mathematical problems. Interscience tracts in pure and appl. Math. No. 8 (1960), New York: Interscience Publishers, New York · Zbl 0086.24101
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