Tohoku Mathematical Journal

A fixed point theorem and its application in ergodic theory

Andrzej Lasota

Full-text: Open access

Article information

Source
Tohoku Math. J. (2) Volume 32, Number 4 (1980), 567-575.

Dates
First available: 3 May 2007

Permanent link to this document
http://projecteuclid.org/euclid.tmj/1178229541

Mathematical Reviews number (MathSciNet)
MR0601927

Zentralblatt MATH identifier
0462.47041

Digital Object Identifier
doi:10.2748/tmj/1178229541

Subjects
Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]
Secondary: 28C10: Set functions and measures on topological groups or semigroups, Haar measures, invariant measures [See also 22Axx, 43A05] 58F11

Citation

Lasota, Andrzej. A fixed point theorem and its application in ergodic theory. Tohoku Mathematical Journal 32 (1980), no. 4, 567--575. doi:10.2748/tmj/1178229541. http://projecteuclid.org/euclid.tmj/1178229541.


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References

  • [1] M. EDELSTEIN, On nonexpansive mappings of Banach spaces, Proc. Cambridge Philos. Soc. 60 (1964), 439-447.
  • [2] S. R. FOGUEL, The Ergodic Theory of Markov Processes, Van Nostrand Reinhold Comp., New York, 1969.
  • [3] E. HOPF, The general temporally discrete Markov processes, J. Rational Mech. Anal. (1954), 13-45.
  • [4] P. KASPROWSKI, On the existence of invariant measures for piecewise convex transfor mations, Ann. Polon. Math, (to appear).
  • [5] K. KRZY^EWSKI AND W. SZLENK, On invariant measures for expanding differentiat mappings, Studia Math. 33 (1969), 83-92.
  • [6] A. LASOTA, On the existence of invariant measures for Markov processes, Ann. Polon Math. 28 (1973), 207-211.
  • [7] G. PIANIGIANI AND J. YoRKE, Expanding maps on set which are almost invariant: deca and chaos, Trans. Amer. Math. Soc. 252 (1979), 351-366.
  • [8] A. RENYI, Representation for real numbers and their ergodic properties, Acta Math Acad. Sci. Hungar. 8 (1957), 477-493.
  • [9] V. A. ROCHLIN, Exact endomorphisms of Lebesgue spaces, Izv. Akad. Nauk SSSR Ser Math. 25 (1961), 499-530. (Amer. Math. Soc. Transl. (2) 39 (1964), 1-36).