uniform mean value theorem

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• Uniform continuity — In mathematical analysis, a function f ( x ) is called uniformly continuous if, roughly speaking, small changes in the input x effect small changes in the output f ( x ) ( continuity ), and furthermore the size of the changes in f ( x ) depends… …   Wikipedia

• Uniform convergence — In the mathematical field of analysis, uniform convergence is a type of convergence stronger than pointwise convergence. A sequence {fn} of functions converges uniformly to a limiting function f if the speed of convergence of fn(x) to f(x) does… …   Wikipedia

• Taylor's theorem — In calculus, Taylor s theorem gives a sequence of approximations of a differentiable function around a given point by polynomials (the Taylor polynomials of that function) whose coefficients depend only on the derivatives of the function at that… …   Wikipedia

• Arzelà–Ascoli theorem — In mathematics, the Arzelà–Ascoli theorem of functional analysis gives necessary and sufficient conditions to decide whether every subsequence of a given sequence of real valued continuous functions defined on a closed and bounded interval has a… …   Wikipedia

• Morera's theorem — If the integral along every C is zero, then ƒ is holomorphic on D. In complex analysis, a branch of mathematics, Morera s theorem, named after Giacinto Morera, gives an important criterion for proving that a function is holomorphic. Morera s… …   Wikipedia

• Singular value decomposition — Visualization of the SVD of a 2 dimensional, real shearing matrix M. First, we see the unit disc in blue together with the two canonical unit vectors. We then see the action of M, which distorts the disk to an ellipse. The SVD decomposes M into… …   Wikipedia

• Central limit theorem — This figure demonstrates the central limit theorem. The sample means are generated using a random number generator, which draws numbers between 1 and 100 from a uniform probability distribution. It illustrates that increasing sample sizes result… …   Wikipedia

• Circular uniform distribution — In probability theory and directional statistics, a circular uniform distribution is a probability distribution on the unit circle whose density is uniform for all angles. Contents 1 Description 2 Distribution of the mean 3 Entropy …   Wikipedia

• Karhunen-Loève theorem — In the theory of stochastic processes, the Karhunen Loève theorem (named after Kari Karhunen and Michel Loève) is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series… …   Wikipedia

• Illustration of the central limit theorem — This article gives two concrete illustrations of the central limit theorem. Both involve the sum of independent and identically distributed random variables and show how the probability distribution of the sum approaches the normal distribution… …   Wikipedia

• Donsker's theorem — In probability theory, Donsker s theorem, named after M. D. Donsker, identifies a certain stochastic process as a limit of empirical processes. It is sometimes called the functional central limit theorem. A centered and scaled version of… …   Wikipedia