About: Gaussian measure

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In mathematics, Gaussian measure is a Borel measure on finite-dimensional Euclidean space Rn, closely related to the normal distribution in statistics. There is also a generalization to infinite-dimensional spaces. Gaussian measures are named after the German mathematician Carl Friedrich Gauss. One reason why Gaussian measures are so ubiquitous in probability theory is the central limit theorem. Loosely speaking, it states that if a random variable X is obtained by summing a large number N of independent random variables of order 1, then X is of order and its law is approximately Gaussian.

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rdfs:label	Gaußsches Maß (de) Mesure gaussienne (fr) Gaussian measure (en) Misura gaussiana (it)
rdfs:comment	In mathematics, Gaussian measure is a Borel measure on finite-dimensional Euclidean space Rn, closely related to the normal distribution in statistics. There is also a generalization to infinite-dimensional spaces. Gaussian measures are named after the German mathematician Carl Friedrich Gauss. One reason why Gaussian measures are so ubiquitous in probability theory is the central limit theorem. Loosely speaking, it states that if a random variable X is obtained by summing a large number N of independent random variables of order 1, then X is of order and its law is approximately Gaussian. (en) Les mesures gaussiennes sont des mesures qui ont une mesure image avec une densité normale sur . (fr) In matematica, una misura gaussiana è una misura di Borel su uno spazio euclideo finito-dimensionale Rn, strettamente correlata alla distribuzione normale in statistica. Esiste anche una generalizzazione a spazi infinito-dimensionali. Le misure gaussiane portano il nome del matematico tedesco Carl Friedrich Gauss. Una ragione per la quale le misure gaussiane sono così diffuse nella teoria della probabilità è il teorema del limite centrale. In parole povere, esso stabilisce che se una variabile casualeX è ottenuta sommando un gran numero N di variabili casuali indipendenti di ordine 1, allora X è di ordine e la sua legge è approssimativamente gaussiana. (it) Als gaußsche Maße bezeichnet man die der Normalverteilung zugrundeliegenden Maße. Der Begriff wird insbesondere auf unendlichdimensionale Räume ausgedehnt. Separable Banachräume mit gaußschen Maße nennt man , welche von eingeführt wurden. Jedoch betrachtete schon Norbert Wiener in seiner ursprünglichen Arbeit einen unendlichdimensionalen Raum, allerdings für reelle Funktionen über dem Einheitsintervall, siehe klassischer Wiener-Raum. (de)
dct:subject	Measures (measure theory) Stochastic processes
Wikipage page ID	6572909 (xsd:integer)
Wikipage revision ID	1104669780 (xsd:integer)
Link from a Wikipage to another Wikipage	Carl Friedrich Gauss Probability distribution Derivative Besov measure Variance Vector space Inner regular measure Invariant (mathematics) Continuous function Mathematics Mean Separable space Germany Equivalence (measure theory) Pushforward measure Statistics Complete measure Path (topology) Mathematician Banach space Central limit theorem Lebesgue measure Locally finite measure Euclidean space Normal distribution Radon–Nikodym derivative Linear functional Radon measure Measures (measure theory) Absolute continuity Abstract Wiener space Stochastic processes Translation (geometry) Weak convergence of measures Dirac measure Borel measure Classical Wiener space Open set Cameron–Martin theorem Support (measure theory) Probability measure Strictly positive measure Borel sigma algebra Push-forward measure There is no infinite-dimensional Lebesgue measure
sameAs	Gaussian measure Gaussian measure Gaussian measure Gaussian measure Gaussian measure Gaussian measure Gaussian measure
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has abstract	Als gaußsche Maße bezeichnet man die der Normalverteilung zugrundeliegenden Maße. Der Begriff wird insbesondere auf unendlichdimensionale Räume ausgedehnt. Separable Banachräume mit gaußschen Maße nennt man , welche von eingeführt wurden. Jedoch betrachtete schon Norbert Wiener in seiner ursprünglichen Arbeit einen unendlichdimensionalen Raum, allerdings für reelle Funktionen über dem Einheitsintervall, siehe klassischer Wiener-Raum. Die Theorie der gaußschen Maße liegt zwischen der Stochastik und der Funktionalanalysis. Sie hat unter anderem Anwendungen im , der Quantenfeldtheorie, der Finanzmathematik sowie der statistischen Physik. (de) In mathematics, Gaussian measure is a Borel measure on finite-dimensional Euclidean space Rn, closely related to the normal distribution in statistics. There is also a generalization to infinite-dimensional spaces. Gaussian measures are named after the German mathematician Carl Friedrich Gauss. One reason why Gaussian measures are so ubiquitous in probability theory is the central limit theorem. Loosely speaking, it states that if a random variable X is obtained by summing a large number N of independent random variables of order 1, then X is of order and its law is approximately Gaussian. (en) Les mesures gaussiennes sont des mesures qui ont une mesure image avec une densité normale sur . (fr) In matematica, una misura gaussiana è una misura di Borel su uno spazio euclideo finito-dimensionale Rn, strettamente correlata alla distribuzione normale in statistica. Esiste anche una generalizzazione a spazi infinito-dimensionali. Le misure gaussiane portano il nome del matematico tedesco Carl Friedrich Gauss. Una ragione per la quale le misure gaussiane sono così diffuse nella teoria della probabilità è il teorema del limite centrale. In parole povere, esso stabilisce che se una variabile casualeX è ottenuta sommando un gran numero N di variabili casuali indipendenti di ordine 1, allora X è di ordine e la sua legge è approssimativamente gaussiana. (it)
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foaf:isPrimaryTopicOf	wikipedia-en:Gaussian_measure
is Link from a Wikipage to another Wikipage of	Probabilistic numerics Besov measure Cylinder set measure Double bubble theorem Inner regular measure Preconditioned Crank–Nicolson algorithm Analysis of Boolean functions Measure (mathematics) Gaussian isoperimetric inequality Ornstein–Uhlenbeck operator Quasi-invariant measure Myhailo Yadrenko Pushforward measure Structure theorem for Gaussian measures Xavier Fernique

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