Journal article
A category-theoretic proof of the ergodic decomposition theorem
- Abstract:
-
The ergodic decomposition theorem is a cornerstone result of dynamical systems and ergodic theory. It states that every invariant measure on a dynamical system is a mixture of ergodic ones. Here we formulate and prove the theorem in terms of string diagrams, using the formalism of Markov categories. We recover the usual measure-theoretic statement by instantiating our result in the category of stochastic kernels. Along the way we give a conceptual treatment of several concepts in the theory o...
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- Publication status:
- Accepted
- Peer review status:
- Peer reviewed
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Authors
Bibliographic Details
- Publisher:
- Cambridge University Press Publisher's website
- Journal:
- Ergodic Theory and Dynamical Systems Journal website
- Acceptance date:
- 2023-01-16
- EISSN:
-
1469-4417
- ISSN:
-
0143-3857
Item Description
- Language:
- English
- Keywords:
- Pubs id:
-
1324818
- Local pid:
- pubs:1324818
- Deposit date:
- 2023-01-22
Terms of use
- Notes:
- This article has been accepted for publication in Ergodic Theory and Dynamical Systems.
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