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Abstract

The basic focus of classical ergodic theory was the development of conditions under which sample or time averages consisting of arithmetic means of a sequence of measurements on a random process converged to a probabilistic or ensemble average of the measurement as expressed by an integral of the measurement with respect to a probability measure. Theorems relating these two kinds of averages are called ergodic theorems.

Keywords

Random Process Integrable Function Ergodic Theorem Prob Ability Discrete Measurement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R. B. Ash, Real Analysis and Probability, Academic Press, New York, 1972.Google Scholar
  2. 2.
    K. L. Chung, A Course in Probability Theory, Academic Press, New York, 1974.MATHGoogle Scholar
  3. 3.
    P. R. Halmos, Measure Theory, Van Nostrand Reinhold, New York, 1950.MATHGoogle Scholar
  4. 4.
    W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, New York, 1964.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • Robert M. Gray
    • 1
  1. 1.Department of Electrical EngineeringStanford UniversityStanfordUSA

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