Map T: X → X on a probability space (X, Σ, μ) such that μ(T⁻¹(A)) = μ(A) for every A ∈ Σ. The base object of ergodic theory; all invariants are computed relative to T.
Measure-preserving transformation
Related concepts
- Probability measure P
- Lebesgue measure
- Lebesgue integral
- Ergodic system
- Birkhoff pointwise ergodic theorem
- Von Neumann mean ergodic theorem
- Poincaré recurrence theorem
- Mixing dynamical system
- Kolmogorov–Sinai entropy
- Koopman operator
- Unique ergodicity
- Ratner measure-rigidity theorems
- Krylov-Bogolyubov theorem
- Arnold's cat map
- Boltzmann transport equation