Define uniformly. uniformly synonyms, uniformly pronunciation, uniformly translation, English dictionary definition of uniformly. adj. 1. Always the same, as in character or degree; unvarying: planks of uniform length. 2. Being the same as or consonant w
In this paper, we mainly consider an infinite tree which has uniformly bounded degrees. Strong law of large numbers for countable Markov chains indexed by an infinite tree with uniformly bounded degree We recall that X is said to be uniformly convex if [delta]([epsilon]) > 0 for all [epsi...
(redirected fromUniformly Ultimately Bounded) AcronymDefinition UubUnunbium(element 112) UubUniformly Ultimately Bounded UubUrban Utility Boundary UubUnion Upper Bound(probability of error) UubUniversity of Ulster at Belfast(University of Ulster)
Let X be a Banach space and let ℒ(X) be the set of all linear bounded operators from X to X. Endowed with the operator norm ||⋅||ℒ(X),defined by ‖U‖ℒ(x)=sup‖x‖≤1‖Ux‖ for each U∈ℒ(X), ℒ(X) is a Banach space. Definition 2.1.1 A family {S(...
is uniformly bounded from above and is bounded away from 0 everywhere but in a small neighbourhood of the critical set \(\mathcal {c}\) , in which df ( x ) approaches 0. as a consequence, we only need to check that the integral of \(\log |df_{\omega }(x)|\) with respect ...
|| is uniformly convex (u.c.) if whenever (xn) ⊂ X and (yn) ⊂ X are bounded sequences in X such that lim 2(||xn||2+||yn||2)−||xn+yn||2=0,then lim||xn−yn||=0.It is obvious from the definition that a uniformly convex norm is locally uniformly ...
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Definition A. 1 Let Q be a self-adjoint, nonnegative definite and bounded linear operator on a separable Hilbert space H. An H-valued stochastic process W={Wt(h);h∈H,t≥0} is called a cylindrical Wiener process on H on the complete probability space (Ω,F,P) if the following condi...
Firstly, we give the definition of Markov chains indexed by an infinite tree with uniformly bounded degree in random environment. Then, we establish some strong limit theorems that are the basis of the main result. Finally, we prove the strong law of large numbers and Shannon-McMillan theorem ...
Prove that f (x) = 1 /(1 + x^2) is uniformly continuous on R by the definition of the uniform continuity. Suppose f is differentiable on (a,b), and |f'| is bounded on (a,b). Prove that f is uniformly continuous on (a,b). Show all work in finding the value of c ...