ergodic theorem
1ergodic theorem — ergodinė teorema statusas T sritis automatika atitikmenys: angl. ergodic theorem vok. Ergodentheorem, n rus. эргодическая теорема, f pranc. théorème d ergodicité, m …
2Maximal ergodic theorem — The maximal ergodic theorem is a theorem in ergodic theory, a discipline within mathematics. Suppose that is a probability space, that is a (possibly noninvertible) measure preserving transformation, and that . Define f * by The …
3Ergodic theory — is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical …
4Ergodic Ramsey theory — is a branch of mathematics where problems motivated by additive combinatorics are proven using ergodic theory.Ergodic Ramsey theory arose shortly after Endre Szemerédi s proof that a set of positive upper density contains arbitrarily long… …
5Ergodic hypothesis — In physics and thermodynamics, the ergodic hypothesis says that, over long periods of time, the time spent by a particle in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e.,… …
6Oseledets theorem — In mathematics, the multiplicative ergodic theorem, or Oseledets theorem provides the theoretical background for computation of Lyapunov exponents of a nonlinear dynamical system. It was proved by Valery Oseledets (also spelled Oseledec ) in 1965 …
7Equidistribution theorem — In mathematics, the equidistribution theorem is the statement that the sequence : a , 2 a , 3 a , ... mod 1 is uniformly distributed on the unit interval, when a is an irrational number. It is a special case of the ergodic theorem.clarify… …
8Birkhoff's theorem (relativity) — In general relativity, Birkhoff s theorem states that any spherically symmetric solution of the vacuum field equations must be stationary and asymptotically flat. This means that the exterior solution must be given by the Schwarzschild metric.The …
9Helmholtz theorem (classical mechanics) — For other uses, see Helmholtz theorem .The Helmholtz theorem of classical mechanics reads as follows:Let:H(x,p;V)=K(p)+varphi(x;V) be the Hamiltonian of a one dimensional system, where :K=frac{p^2}{2m} is the kinetic energy and :varphi(x;V) is a… …
10Stationary ergodic process — In probability theory, stationary ergodic process is a stochastic process which exhibits both stationarity and ergodicity. In essence this implies that the random process will not change its statistical properties with time.Stationarity is the… …
