Measures (measure theory) | Dynamical systems

Invariant measure

In mathematics, an invariant measure is a measure that is preserved by some function. The function may be a geometric transformation. For examples, circular angle is invariant under rotation, hyperbolic angle is invariant under squeeze mapping, and a difference of slopes is invariant under shear mapping. Ergodic theory is the study of invariant measures in dynamical systems. The Krylov–Bogolyubov theorem proves the existence of invariant measures under certain conditions on the function and space under consideration. (Wikipedia).

Invariant measure
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Related pages

Lebesgue measure | If and only if | Angle | Stochastic differential equation | Squeeze mapping | Transfer operator | Geometric transformation | Krylov–Bogolyubov theorem | Determinant | Measurable space | Shear mapping | Ergodic theory | Mathematics | Function (mathematics) | Isometry | Markov chain | Measurable function | Euclidean space | Convex combination | Convex set | Probability measure | Orthogonal matrix | Haar measure | Hyperbolic angle | Random variable | Special linear group | Area | Slope | Measure (mathematics) | Pushforward measure | Locally compact group | Monoid