In mathematics, Gaussian measure is a Borel measure on finite-dimensional Euclidean space R n {\displaystyle R^{n}} , closely related to the normal distribution...

push-forward and the standard Gaussian measure on the real line: a Borel measure γ on a separable Banach space X is called Gaussian if the push-forward of γ...

along a circular Gaussian beam of a given wavelength and polarization are determined by two parameters: the waist w0, which is a measure of the width of...

per matrix element. The Gaussian unitary ensemble GUE ( n ) {\displaystyle {\text{GUE}}(n)} is described by the Gaussian measure with density 1 Z GUE (...

In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f ( x ) = exp ⁡ ( − x 2 ) {\displaystyle f(x)=\exp(-x^{2})}...

in the case of a hyperboloid or the inside of a torus. Gaussian curvature is an intrinsic measure of curvature, depending only on distances that are measured...

theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional...

In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued...

construction developed by Leonard Gross to understand the structure of Gaussian measures on infinite-dimensional spaces. The construction emphasizes the fundamental...

processing, a Gaussian filter is a filter whose impulse response is a Gaussian function (or an approximation to it, since a true Gaussian response would...

for Gaussian measures shows that the abstract Wiener space construction is essentially the only way to obtain a strictly positive Gaussian measure on a...

equipped with a Gaussian measure γ. As stated in the article on the Vitali covering theorem, the Vitali covering theorem fails for Gaussian measures on infinite-dimensional...

include: Borel measure, Jordan measure, ergodic measure, Gaussian measure, Baire measure, Radon measure, Young measure, and Loeb measure. In physics an...

Gaussian units constitute a metric system of physical units. This system is the most common of the several electromagnetic unit systems based on cgs...

space. An example is the Gaussian cylinder set measure on Hilbert space. Cylinder set measures are in general not measures (and in particular need not...

measure on any topological space; Gaussian measure on Euclidean space ℝn with its Borel sigma algebra; Probability measures on the σ-algebra of Borel sets...

In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of...

The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function f ( x ) = e − x 2 {\displaystyle f(x)=e^{-x^{2}}}...

Consider a collection of Gaussian measures Γ = { γ i | i ∈ I } , {\displaystyle \Gamma =\{\gamma _{i}|i\in I\},} where the measure γ i {\displaystyle \gamma...

Probability Theory for Analysts. Chapman and Hall. Gaussian measure, a finite-dimensional Borel measure Feller, William (1971), An introduction to probability...

Gauss–Markov process Gauss–Markov theorem Gaussian copula Gaussian measure Gaussian correlation inequality Gaussian isoperimetric inequality Gauss's inequality...

canonical Gaussian cylinder set measure on the Cameron-Martin Hilbert space corresponding to C0. Classical Wiener measure is a Gaussian measure: in particular...

convex geometry. The Gaussian correlation inequality states: Let μ {\displaystyle \mu } be an n-dimensional Gaussian probability measure on R n {\displaystyle...

certain elements of the Cameron–Martin Hilbert space. The standard Gaussian measure γ n {\displaystyle \gamma ^{n}} on n {\displaystyle n} -dimensional...

of Borel measure Structure theorem for Gaussian measures – Mathematical theorem Projection-valued measure – Mathematical operator-value measure of interest...

among all sets of given Gaussian measure in the n-dimensional Euclidean space, half-spaces have the minimal Gaussian boundary measure. Let A {\displaystyle...

Infinite-Dimensional Calculus, Introduction to Stochastic Integration, Gaussian Measures in Banach Spaces, and White Noise Distribution Theory and served as...

counting measure for discrete distributions, or Lebesgue measure or a convenient variant thereof like Gaussian measure or the uniform measure on the sphere...

theorem can be used, for example, to determine whether a translate of a Gaussian measure μ {\displaystyle \mu } is equivalent to μ {\displaystyle \mu } (only...

a Gaussian measure on an infinite-dimensional space. It is now known that logarithmic Sobolev inequalities hold for many different types of measures, not...