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.
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References
R. B. Ash, Real Analysis and Probability, Academic Press, New York, 1972.
K. L. Chung, A Course in Probability Theory, Academic Press, New York, 1974.
P. R. Halmos, Measure Theory, Van Nostrand Reinhold, New York, 1950.
W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, New York, 1964.
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© 1988 Springer Science+Business Media New York
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Gray, R.M. (1988). Averages. In: Probability, Random Processes, and Ergodic Properties. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2024-2_4
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DOI: https://doi.org/10.1007/978-1-4757-2024-2_4
Publisher Name: Springer, New York, NY
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