invariant measure


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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.
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1](X), called invariant measure of the IFSP(w,p), such that M[bar.
alpha]] (N, [omega]) to the properties of the invariant measure, and of its orthogonal polynomials.
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.
extends to a shift invariant measure on S (Dynkin, 1969).
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.
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.
In Section 5, we provide an example of how this theorem allows us to transmit results concerning conservation laws over to invariant measures.
The theory is then applied, in five chapters on invariant measures, Lattice systems, stochastic Burgers equation, an environmental pollution model, and in six bond market models.