Abstract
In the previous chapters we looked at topological dynamical systems, but now let us turn to dynamical systems that preserve some probability measure on the state space. We shall first motivate this change of perspective.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
…many results of pure mathematics, which though likewise apparently fruitless at first, later become useful in practical science as soon as our mental horizon has been broadened …
- 2.
Vorlesungen über Gastheorie, I. Theil, Verlag von Johann Ambrosius Barth, Leipzig, 1896, Vorwort ⋅ Translation by Stephen G. Brush, Lectures on Gas Theory, University of California Press, 1964 ⋅ Foreword to Part I.
Bibliography
A. Baker [1984] A Concise Introduction to the Theory of Numbers, Cambridge University Press, Cambridge, 1984.
[1981] Probability Theory and Elements of Measure Theory, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], London, 1981. 2nd edition of the translation by R. B. Burckel from the 3rd German edition, Probability and Mathematical Statistics.
[1979] Probability and Measure, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York-Chichester-Brisbane, 1979.
V. I. Bogachev [2007] Measure Theory. Vol. I, II, Springer-Verlag, Berlin, 2007.
A. Deitmar and S. Echterhoff [2009] Principles of Harmonic Analysis, Universitext, Springer, New York, 2009.
S. N. Ethier and T. G. Kurtz [1986] Markov Processes, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons Inc., New York, 1986.
G. B. Folland [1995] A Course in Abstract Harmonic Analysis, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995.
E. Hewitt and K. A. Ross [1979] Abstract Harmonic Analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften, vol. 115, Springer-Verlag, Berlin, 1979.
S. Lang [1993] Real and Functional Analysis, 3rd ed., Graduate Texts in Mathematics, vol. 142, Springer-Verlag, New York, 1993.
L. Nachbin [1976] The Haar Integral, Robert E. Krieger Publishing Co., Huntington, NY, 1976. Translated from the Portuguese by L. Bechtolsheim, Reprint of the 1965 edition.
W. Rudin [1987] Real and Complex Analysis, 3rd ed., McGraw-Hill Book Co., New York, NY, 1987.
C. E. Silva [2008] Invitation to Ergodic Theory, Student Mathematical Library, vol. 42, American Mathematical Society, Providence, RI, 2008.
A. Weil [1940] L’Intégration dans les Groupes Topologiques et ses Applications, Actual. Sci. Ind., no. 869, Hermann et Cie., Paris, 1940. [This book has been republished by the author at Princeton, N. J., 1941.].
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Tanja Eisner, Bálint Farkas, Markus Haase, and Rainer Nagel
About this chapter
Cite this chapter
Eisner, T., Farkas, B., Haase, M., Nagel, R. (2015). Measure-Preserving Systems. In: Operator Theoretic Aspects of Ergodic Theory. Graduate Texts in Mathematics, vol 272. Springer, Cham. https://doi.org/10.1007/978-3-319-16898-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-16898-2_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16897-5
Online ISBN: 978-3-319-16898-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)