Strong convergence
Encyclopedia
In mathematics
, strong convergence may refer to:
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, strong convergence may refer to:
- The strong convergence of random variablesConvergence of random variablesIn probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes...
of a probability distributionProbability distributionIn probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
. - The strong convergenceWeak convergence (Hilbert space)In mathematics, weak convergence in a Hilbert space is convergence of a sequence of points in the weak topology.-Definition:A sequence of points in a Hilbert space H is said to converge weakly to a point x in H if...
of a sequence in a Hilbert spaceHilbert spaceThe mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...
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