In probability theory, Lévy’s continuity theorem, or Lévy's convergence theorem, named after the French mathematician Paul Lévy, connects convergence in...

decomposition theorem Lévy distribution Lévy metric Lévy's modulus of continuity Lévy–Prokhorov metric Lévy's continuity theorem Lévy's zero-one law Concentration...

1 ) {\textstyle {\mathcal {N}}(0,1)} , which implies through Lévy's continuity theorem that the distribution of Z n {\textstyle Z_{n}} will approach...

the continuity theorem may refer to one of the following results: the Lévy continuity theorem on random variables; the Kolmogorov continuity theorem on...

Lévy's modulus of continuity theorem is a theorem that gives a result about an almost sure behaviour of an estimate of the modulus of continuity for Wiener...

functors Graph continuity, for payoff functions in game theory Continuity theorem may refer to one of two results: Lévy's continuity theorem, on random variables...

variables: a classical proof of the Central Limit Theorem uses characteristic functions and Lévy's continuity theorem. Another important application is to the...

convergence of measures Helly–Bray theorem Slutsky's theorem Skorokhod's representation theorem Lévy's continuity theorem Uniform integrability Markov's inequality...

(mathematical series) Le Cam's theorem (probability theory) Lévy continuity theorem (probability) Lévy's modulus of continuity theorem (probability) Martingale...

limit theorem / (L:DC) Lindeberg's condition Lyapunov's central limit theorem / (L:R) Lévy's continuity theorem / anl (L:R) Lévy's convergence theorem / (S:R)...

{\displaystyle L^{1}} . This result is usually called Lévy's zero–one law or Levy's upwards theorem. The reason for the name is that if A {\displaystyle...

Laboratory quality control Lévy's convergence theorem Lévy's continuity theorem Lévy arcsine law Lévy distribution Lévy flight Lévy process Lewontin's Fallacy...

convergence in distribution of {Xn + Yn} to X + Y or of {XnYn} to XY. Lévy’s continuity theorem: The sequence {Xn} converges in distribution to X if and only...

characteristic function of the constant random variable μ, and hence by the Lévy continuity theorem, X ¯ n {\displaystyle {\overline {X}}_{n}} converges in distribution...

In measure theory Prokhorov's theorem relates tightness of measures to relative compactness (and hence weak convergence) in the space of probability measures...

behaved (with respect to continuity) that all of its restrictions to all possible dense subsets are discontinuous. The theorem's conclusion becomes more...

limit theorems. Examples of continuous distributions that are infinitely divisible are the normal distribution, the Cauchy distribution, the Lévy distribution...

the Lévy–Khintchine theorem suggests that every Lévy process is the sum of Brownian motion with drift and another independent random variable, a Lévy jump...

{\displaystyle P(A_{k}{\text{ i.o.}})>0.} Lévy's zero–one law Kuratowski convergence Infinite monkey theorem E. Borel, "Les probabilités dénombrables et...

immediately from the definitions, but its continuity is a very special fact – a special case of a general theorem stating that all Brownian martingales are...

limit, or to diverge. These claims are the content of the Riemann series theorem. A historically important example of conditional convergence is the alternating...

The following dual representation of W1 is a special case of the duality theorem of Kantorovich and Rubinstein (1958): when μ and ν have bounded support...

counterexample in analysis, because it challenges naive intuitions about continuity, derivative, and measure. Although it is continuous everywhere, and has...

\geq \alpha } and f ( β ) = β {\displaystyle f(\beta )=\beta } . The continuity of the normal function implies the class of fixed points is closed (the...

defines a family of stable distributions. By the classical central limit theorem the properly normed sum of a set of random variables, each with finite...

{\displaystyle X_{t}} is also a Gaussian process. In other cases, the central limit theorem indicates that X t {\displaystyle X_{t}} will be approximately normally...

uniformly distributed random phase. Where applicable, the central limit theorem dictates that at any point, the sum of these individual plane-wave contributions...

is the Runge–Gross (RG) theorem (1984) – the time-dependent analogue of the Hohenberg–Kohn (HK) theorem (1964). The RG theorem shows that, for a given...

conjecture Cartan–Hadamard theorem Collapsing manifold Lévy–Gromov inequality Taubes's Gromov invariant Mostow rigidity theorem Ramsey–Dvoretzky–Milman phenomenon...

and local martingale property. Uniqueness follows from the Lipschitz continuity of σ , b {\displaystyle \sigma \!,\!b} . In fact, L a ; b + ∂ ∂ s {\displaystyle...