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There is a page named "Measure-preserving transformation" on Wikipedia
- thermodynamic equilibrium. A measure-preserving dynamical system is defined as a probability space and a measure-preserving transformation on it. In more detail...23 KB (3,592 words) - 13:02, 9 August 2024
- Isometry (redirect from Length-preserving transformation)mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective...18 KB (2,351 words) - 20:34, 29 July 2024
- is said to be a measure-preserving transformation of X , if it is a map from X to itself, it is Σ-measurable, and is measure-preserving. The triplet (T...52 KB (7,067 words) - 22:55, 8 June 2024
- Ergodic theory (redirect from Ergodic transformation)they preserve the measure that is density. The formal definition is as follows: Let T : X → X be a measure-preserving transformation on a measure space...26 KB (3,727 words) - 09:42, 19 February 2024
- the outcomes are independent, the shift preserves the measure, and thus T is a measure-preserving transformation. The quadruplet ( X , A , μ , T ) {\displaystyle...11 KB (1,739 words) - 18:15, 12 March 2023
- of several formal mathematical definitions. For example, a measure-preserving transformation T is said to be strong mixing if lim k → ∞ μ ( T − k A ∩ B...5 KB (616 words) - 00:35, 8 August 2024
- X {\displaystyle T:X\to X} is a (possibly noninvertible) measure-preserving transformation, and that f ∈ L 1 ( μ , R ) {\displaystyle f\in L^{1}(\mu...1 KB (190 words) - 03:37, 13 March 2024
- \Sigma ,\mu )} be a finite measure space and let f : X → X {\displaystyle f\colon X\to X} be a measure-preserving transformation. Below are two alternative...12 KB (1,789 words) - 17:31, 24 July 2024
- Ergodicity (redirect from Ergodic measure)space, only its distribution. Such a system is "measure-preserving" (area-preserving, volume-preserving). A formal difficulty arises when one tries to...54 KB (8,846 words) - 03:02, 17 August 2024
- velocity while preserving its magnitude, and exchanging primed and unprimed variables, always applies to finding the inverse transformation of every boost...103 KB (14,094 words) - 22:06, 27 May 2024
- Monotonic function (redirect from Order-preserving)function being preserved across a monotonic transform (see also monotone preferences). In this context, the term "monotonic transformation" refers to a...19 KB (2,467 words) - 19:43, 4 August 2024
- orientation-preserving orthogonal transformation). Indeed, when an orthogonal transformation matrix produces a reflection, its determinant is −1. A measure of...9 KB (1,143 words) - 22:01, 2 May 2024
- \textstyle {\bigcap _{n=1}^{\infty }G_{n}}} . An invertible measure-preserving transformation on a standard probability space that obeys the 0-1 law is...6 KB (896 words) - 17:24, 27 April 2024
- Krieger, Wolfgang (1970). "On entropy and generators of measure-preserving transformations". Transactions of the American Mathematical Society. 149 (2):...64 KB (7,285 words) - 18:50, 12 August 2024
- mathematics, an invariant measure is a measure that is preserved by some function. The function may be a geometric transformation. For examples, circular...5 KB (851 words) - 04:46, 28 November 2023
- and Wintner (1941). Suppose that τ is a measure-preserving transformation of a measure space S with finite measure. If f is a real-valued integrable function...2 KB (234 words) - 18:52, 19 July 2022
- applies. An important special case of conservative systems are the measure-preserving dynamical systems. Informally, dynamical systems describe the time...12 KB (1,808 words) - 02:58, 25 November 2023
- Statistical dispersion (redirect from Measure of dispersion)measurements are in metres or seconds, so is the measure of dispersion. Examples of dispersion measures include: Standard deviation Interquartile range...7 KB (936 words) - 23:55, 23 June 2024
- any measure-preserving transformation T {\displaystyle T} of the probability space (Ω, β, μ) and A ∈ β {\displaystyle A\in \beta } of positive measure there...7 KB (1,053 words) - 03:52, 30 June 2024
- Grigorchuk's group G was constructed as a group of Lebesgue-measure-preserving transformations on the unit interval, but subsequently simpler descriptions...19 KB (2,700 words) - 20:48, 9 August 2024
- The Transformation of the Electrodynamical Equations (1909) by Harry Bateman 686700The Transformation of the Electrodynamical Equations1909Harry Bateman
- different holistic properties, such a transformation can be carried through locally, but there is no single transformation for the whole surface. ...the stereographic
- note the angular measure of these transformations. The classical and modern transformations for linear motion also have angular measures: differences of