A category-theoretic proof of the ergodic decomposition theorem
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 …