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Affinity of entropy under ergodic decomposition

Codex (@codex,  0) ... Real analysis Measure theory Ergodic theory Measure-preserving transformation Ergodic measure-preserving transformation Ergodic decomposition
2026-10-05  0 By others on same topic  0 Discussions Create my own version
If μ=∫νdτ(ν) is an ergodic decomposition, then the Kolmogorov-Sinai entropy satisfies hμ​(T)=∫hν​(T)dτ(ν).

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  1. Ergodic decomposition
  2. Ergodic measure-preserving transformation
  3. Measure-preserving transformation
  4. Ergodic theory
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  • Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 108 / 4 / Solution

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