## On the existence of invariant measures for piecewise monotonic transformations.(English)Zbl 0298.28015

### MSC:

 28D05 Measure-preserving transformations 47A35 Ergodic theory of linear operators 54H20 Topological dynamics (MSC2010)
Full Text:

### References:

 [1] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. · Zbl 0084.10402 [2] A. O. Gel$$^{\prime}$$fond, A common property of number systems, Izv. Akad. Nauk SSSR. Ser. Mat. 23 (1959), 809 – 814 (Russian). [3] A. Lasota, Invariant measures and functional equations, Aequationes Math. 9 (1973), 193 – 200. · Zbl 0269.28008 [4] W. Parry, On the \?-expansions of real numbers, Acta Math. Acad. Sci. Hungar. 11 (1960), 401 – 416 (English, with Russian summary). · Zbl 0099.28103 [5] A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar 8 (1957), 477 – 493. · Zbl 0079.08901 [6] V. A. Rohlin, Exact endomorphisms of a Lebesgue space, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961), 499 – 530 (Russian). [7] S. M. Ulam, A collection of mathematical problems, Interscience Tracts in Pure and Applied Mathematics, no. 8, Interscience Publishers, New York-London, 1960. · Zbl 0086.24101 [8] Michael S. Waterman, Some ergodic properties of multi-dimensional \?-expansions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 16 (1970), 77 – 103. · Zbl 0199.37102 [9] André Avez, Propriétés ergodiques des endomorphisms dilatants des variétés compactes, C. R. Acad. Sci. Paris Sér. A-B 266 (1968), A610 – A612 (French). · Zbl 0186.56704 [10] K. Krzyżewski and W. Szlenk, On invariant measures for expanding differentiable mappings, Studia Math. 33 (1969), 83 – 92. · Zbl 0176.00901
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.