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almost continuous function

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  • Continuous mapping theorem — In probability theory, the continuous mapping theorem states that continuous functions are limit preserving even if their arguments are sequences of random variables. A continuous function, in Heine’s definition, is such a function that maps… …   Wikipedia

  • Continuous functional calculus — In mathematics, the continuous functional calculus of operator theory and C* algebra theory allows applications of continuous functions to normal elements of a C* algebra. More precisely, Theorem. Let x be a normal element of a C* algebra A with… …   Wikipedia

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  • Almost everywhere — In measure theory (a branch of mathematical analysis), one says that a property holds almost everywhere if the set of elements for which the property does not hold is a null set, i.e. is a set with measure zero, or in cases where the measure is… …   Wikipedia

  • Dirac delta function — Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function. The other convention… …   Wikipedia

  • Characteristic function (probability theory) — The characteristic function of a uniform U(–1,1) random variable. This function is real valued because it corresponds to a random variable that is symmetric around the origin; however in general case characteristic functions may be complex valued …   Wikipedia

  • Differentiable function — A differentiable function The absolute value function is not …   Wikipedia

  • Sample continuous process — In mathematics, a sample continuous process is a stochastic process whose sample paths are almost surely continuous functions.DefinitionLet ( Omega;, Sigma;, P) be a probability space. Let X : I times; Omega; rarr; S be a stochastic process,… …   Wikipedia

  • Probability density function — Boxplot and probability density function of a normal distribution N(0, σ2). In probability theory, a probability density function (pdf), or density of a continuous random variable is a function that describes the relative likelihood for this… …   Wikipedia

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