In mathematics, an invariant measure is a measure that is preserved by some function. The function may be a geometric transformation. For examples, circular...

In mathematics, a quasi-invariant measure μ with respect to a transformation T, from a measure space X to itself, is a measure which, roughly speaking...

a measure μ on X that the map f leaves unchanged, a so-called invariant measure, i.e one for which f∗(μ) = μ. One can also consider quasi-invariant measures...

σ-finite quasi-invariant measure μ on X which is unique up to measure equivalence (that is any two such measures have the same sets of measure zero). If...

ergodicity carries over unchanged if one replaces invariant measures by quasi-invariant measures. Important examples are the action of a semisimple Lie group (or...

measure on some measurable space (X, Σ). A measure ν is the trivial measure μ if and only if ν(X) = 0. μ is an invariant measure (and hence a quasi-invariant...

theory, a Sinai–Ruelle–Bowen (SRB) measure is an invariant measure that behaves similarly to, but is not an ergodic measure. In order to be ergodic, the time...

mathematics, cylinder set measure (or promeasure, or premeasure, or quasi-measure, or CSM) is a kind of prototype for a measure on an infinite-dimensional...

central tendency (or measure of central tendency) is a central or typical value for a probability distribution. Colloquially, measures of central tendency...

representation, G acts on functions on G/H. If however Haar measures give rise only to a quasi-invariant measure on G/H, certain 'correction factors' have to be made...

are quasi-isometric. This quasi-isometry class is thus an invariant of the group G. Any property of metric spaces that only depends on a space's quasi-isometry...

simple spectrum. In collaboration with B. S. Mityagin he worked on quasi-invariant measures on topological linear spaces. Around 1960 the problems of optimal...

the entropy of a discrete variable is location-invariant and scale-independent, and therefore not a measure of dispersion in the above sense, the entropy...

symmetric difference of an open set in X with a set of measure zero, for a certain (quasi)invariant measure on X. A fundamental domain always contains a free...

for a general topological space, but it is nevertheless topologically invariant since it is equivalent to compactness.) One example of a compact space...

finite invariant measure on X, but the dynamics of the system is constrained to the level sets of I on X, hence the system possesses invariant sets of...

important convergence results. In short, we need the existence of invariant measure and Harris recurrent to establish the Law of Large Numbers of MCMC...

} is a quasi-invariant measure on X = G / H {\displaystyle X=G/H} . It is not assumed that | ψ ⟩ {\displaystyle |\psi \rangle } be invariant up to a...

\mu } is the trivial (zero) measure. (See quasi-invariant measure.) In fact, γ {\displaystyle \gamma } is quasi-invariant under translation by an element...

turn that any quasi-isometrically invariant property satisfied by the word metric of G or by any model space of G is an isomorphism invariant of G. Modern...

probability measure on R such that the null sets are translation invariant, it suffices to show that ν is quasi-equivalent to Lebesgue measure, i.e. that...

mathematics for his classification of P {\displaystyle P} -invariant and stationary measures for the moduli of translation surfaces, in joint work with...

of the posterior density with respect to some reference measure, typically the Lebesgue measure. The MAP can be used to obtain a point estimate of an unobserved...

{\displaystyle L^{p}} norms, are invariant under arbitrary rearrangements of the values of a function. The Lorentz space on a measure space ( X , μ ) {\displaystyle...

numerical invariant of G {\displaystyle G} , the minimum height of a Trémaux tree for a supergraph of G {\displaystyle G} . This invariant and its close...

Penrose's quasi-local energy–momentum based on twistor methods, the field is still in flux. Eventually, the hope is to use a suitable defined quasi-local...

uniquely determined if U is minimal, i.e. K is the smallest closed subspace invariant under U and U* containing H. In fact define H = H ⊕ H ⊕ H ⊕ ⋯ , {\displaystyle...

continuous functions C(M), we only recover M topologically. The algebraic invariant that recovers the Riemannian structure is a spectral triple. It is constructed...

published on moduli spaces, with a theory summed up in his book Geometric Invariant Theory, on the equations defining an abelian variety, and on algebraic...

generated quasi-Fuchsian groups are conjugate to Fuchsian groups under quasi-conformal transformations. The limit set is contained in the invariant Jordan...