In mathematics, uniform integrability is an important concept in real analysis, functional analysis and measure theory, and plays a vital role in the...

Lp in terms of convergence in measure and a condition related to uniform integrability. Let ( X , A , μ ) {\displaystyle (X,{\mathcal {A}},\mu )} be a...

condition that there is a dominating integrable function g {\displaystyle g} can be relaxed to uniform integrability of the sequence (fn), see Vitali convergence...

the negative part might also be plus infinity. Let ε > 0. Due to uniform integrability with respect to the conditional expectation, there exists a c > 0...

is the Arzelà–Ascoli theorem. Other cases of interest relate to uniform integrability, and the concept of normal family in complex analysis. Mahler's...

| = 0. {\displaystyle \lim _{n}\operatorname {E} |X_{n}-X|=0.} Uniform integrability: In some cases, the equality lim n E ⁡ [ X n ] = E ⁡ [ lim n X n...

Riemann integrability, and, with additional hypotheses, differentiability, are transferred to the limit f {\displaystyle f} if the convergence is uniform, but...

In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions...

needed] If fn is a uniformly convergent sequence on [a, b] with limit f, then Riemann integrability of all fn implies Riemann integrability of f, and ∫ a b...

mathematics, a real function f {\displaystyle f} of real numbers is said to be uniformly continuous if there is a positive real number δ {\displaystyle \delta...

previous term relative to the noise. This results in a "smoothing" or integration of the output, similar to a low pass filter. For an AR(2) process, the...

School uniforms in different countries School uniform is a practice that dates to the 16th century in England. Charity schools such Christ's Hospital,...

integrals. There are different methods to perform a Monte Carlo integration, such as uniform sampling, stratified sampling, importance sampling, sequential...

obtain convergence in L1 (i.e., convergence in mean), one requires uniform integrability of the random variables N t {\displaystyle N_{t}} . By Chebyshev's...

theorem Skorokhod's representation theorem Lévy's continuity theorem Uniform integrability Markov's inequality Chebyshev's inequality = Chernoff bound Chernoff's...

} This lack of uniform integrability is behind many divergence phenomena for the Fourier series. For example, together with the uniform boundedness principle...

the sum of a large number of plane, cylindrical or spherical waves with uniformly distributed random phase. Where applicable, the central limit theorem...

Leskelä, L.; Vihola, M. (2013). "Stochastic order characterization of uniform integrability and tightness". Statistics and Probability Letters. 83 (1): 382–389...

following properties. Let a i j ( x , t ) {\displaystyle a^{ij}(x,t)} be uniformly continuous coefficients and b i ( x , t ) {\displaystyle b^{i}(x,t)} be...

The Uniform Civil Code is a proposal in India to formulate and implement personal laws of citizens which apply equally to all citizens, regardless of...

not for very low strikes (it becomes negative or the density does not integrate to one). One possibility to "fix" the formula is use the stochastic collocation...

X_{n}{\xrightarrow {\overset {}{P}}}X} and the sequence (Xn) is uniformly integrable. If X n   → p   X {\displaystyle X_{n}\ \xrightarrow {\overset {}{p}}...

well as a nationwide uniform integration test and higher quality standards. In addition, on the same day, it passed the Integration Year Act, which provides...

The uniforms and insignia of the Schutzstaffel (SS) served to distinguish its Nazi paramilitary ranks between 1925 and 1945 from the ranks of the Wehrmacht...

{\displaystyle \{Z_{T}\mid T{\text{ a finite-valued stopping time}}\}} is uniformly integrable. Let Z {\displaystyle Z} be a cadlag supermartingale of class D....

this would only be the case if the Radon–Nikodym derivative were a uniformly integrable martingale, which the exponential martingale described above is not...

The Uniform Commercial Code (UCC), first published in 1952, is one of a number of uniform acts that have been established as law with the goal of harmonizing...

"Victory Blue" uniforms, worn by the Cardinals during the late 1970s and 1980s, would be returning for the 2019 season. The uniforms, integrating the powder...

383–399, MR 1489400 Alibert, J. J.; Bouchitté, G. (1997), "Non-uniform integrability and generalized Young measures", Journal of Convex Analysis, 4 (1):...

typed lambda calculus Rho calculus, introduced as a general means to uniformly integrate rewriting into lambda calculus Process calculus, a set of approaches...