- invariant measure
- мат.инвариантная мера
English-Russian scientific dictionary. 2008.
invariant measure
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Invariant measure — In mathematics, an invariant measure is a measure that is preserved by some function. Invariant measures are of great interest in the study of dynamical systems. The Krylov Bogolyubov theorem proves the existence of invariant measures under… … Wikipedia
Quasi-invariant measure — In mathematics, a quasi invariant measure mu; with respect to a transformation T , from a measure space X to itself, is a measure which, roughly speaking, is multiplied by a numerical function by T . An important class of examples occurs when X… … Wikipedia
Measure (mathematics) — Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0. In mathematical analysis … Wikipedia
Invariant (mathematics) — In mathematics, an invariant is a property of a class of mathematical objects that remains unchanged when transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually… … Wikipedia
Invariant theory — is a branch of abstract algebra that studies actions of groups on algebraic varieties from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit description of polynomial functions that do not … Wikipedia
Measure-preserving dynamical system — In mathematics, a measure preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Contents 1 Definition 2 Examples 3 Homomorphisms 4 … Wikipedia
Invariant speed — The invariant speed or observer invariant speed is the speed an object or particle must be traveling at for its speed to have the same measure in all reference frames. The invariance of the speed of light is a consequence of the postulates of… … Wikipedia
Haar measure — In mathematical analysis, the Haar measure is a way to assign an invariant volume to subsets of locally compact topological groups and subsequently define an integral for functions on those groups.This measure was introduced by Alfréd Haar, a… … Wikipedia
There is no infinite-dimensional Lebesgue measure — In mathematics, it is a theorem that there is no analogue of Lebesgue measure on an infinite dimensional space. This fact forces mathematicians studying measure theory on infinite dimensional spaces to use other kinds of measures: often, the… … Wikipedia
Pushforward measure — In mathematics, a pushforward measure (also push forward or push forward) is obtained by transferring ( pushing forward ) a measure from one measurable space to another using a measurable function.DefinitionGiven measurable spaces ( X 1, Sigma;1) … Wikipedia
Trivial measure — In mathematics, specifically in measure theory, the trivial measure on any measurable space ( X , Σ) is the measure μ which assigns zero measure to every measurable set: μ ( A ) = 0 for all A in Σ.Properties of the trivial measureLet μ denote the … Wikipedia
