| 41. | Ergodic theory considers measures that are invariant under, or arise naturally from, a dynamical system.
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| 42. | Thus, hypertext fiction of the simple node and link variety is ergodic literature but not cybertext.
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| 43. | Ergodic literature is not defined by medium, but by the way in which the text functions.
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| 44. | The concept appears in ergodic theory the study of stochastic processes and measure-preserving dynamical systems.
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| 45. | A conceptually different proof of the multiplicative ergodic theorem was found by M . S . Raghunathan.
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| 46. | In physics the term is used to imply that a system satisfies the ergodic hypothesis of thermodynamics.
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| 47. | Bourgain was awarded the Fields Medal in 1994, in part for this work in ergodic theory.
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| 48. | The limit exists as the logarithm of the complexity function is uniformly recurrent or even uniquely ergodic.
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| 49. | This is because under ergodic assumptions the long-term average of surprise is entropy.
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| 50. | Arithmetic combinatorics arose out of the interplay between number theory, combinatorics, ergodic theory and harmonic analysis.
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