invariant measure


Also found in: Wikipedia.

invariant measure

[in′ver·ē·ənt ′mezh·ər]
(mathematics)
A Borel measure m on a topological space X is invariant for a transformation group (G,X,π) if for all Borel sets A in X and all elements g in G, m (Ag ) = m (A), where Ag is the set of elements equal to π(g,x) for some x in A.
Mentioned in ?
References in periodicals archive ?
We will also prove the existence and uniqueness of an invariant measure which satisfies a ldp.
1](X), called invariant measure of the IFSP(w,p), such that M[bar.
In the case of a unique equilibrium, stochastic stability is proved and a formula for the perturbed invariant measure was produced in terms of the quasi-potential.
alpha]] (N, [omega]) to the properties of the invariant measure, and of its orthogonal polynomials.
2 that, for an ergodic Hamiltonian system, [Mu], is the only invariant measure on [S.
mu]][member of] M(X), the so-called invariant measure of the IFSP (w, p), such that [bar.
s] = 1, and let [micro] be the associated invariant measure.
The involved quantity is the invariant measure of an M/G/1/C queue with arrivals by batches with distribution the mouse size distribution.
This is the first full-length look at Markov semigroups both in spaces of bounded and continuous functions as well as in Lp spaces relevant to the invariant measure of the semigroup.
He covers Tonelli Lagrangians and Hamiltonians on compact manifolds, from KAM theory to Aubry-Mather theory, action-minimizing invariant measures for Tonelli Lagrangians, action-minimizing curves for Tonelli Lagrangians, and the Hamtonian-Jacobi equation and weak KAM theory.
Barreira (Instituto Superior Tecnico, Lisbon) and Pesin (Pennsylvania State University) introduce the ergodic properties of smooth dynamical systems on Riemannian manifolds with respect to natural invariant measures, focusing on systems whose trajectories are hyperbolic and Lyapunov exponents.
Invariant measures and convergence properties for cellular automaton 184 and related processes.