Invariant Measures for Continuous Maps

  • Manfred Einsiedler
  • Thomas Ward


Continuous maps on compact metric spaces are an important source of examples of measure-preserving transformations. In this chapter the basic properties of such maps are studied, and the ergodic decomposition is introduced. Equidistribution and generic orbits are introduced, and Furstenberg’s proof of Weyl’s equidsitrubution theorem for polynomials with an irrational coefficient is given.


Invariant Measure Ergodic Theorem Invariant Probability Measure Ergodic Measure Unique Ergodicity 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Departement MathematikETH ZurichZurichSwitzerland
  2. 2.School of MathematicsUniversity of East AngliaNorwichUK

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