Sentence examples for generalized limits from inspiring English sources

It is well known that a convergent sequence is almost convergent such that its ordinary and generalized limits are equal.

Note that a convergent sequence is almost convergent and its limit and its generalized limit both are identical, but an almost convergent sequence need not be convergent.

In 1948, Lorentz [1] used this notion of a generalized limit to define a new type of convergence, known as almost convergence.

A sequence x = ( x k ) ∈ ℓ ∞ is said to be almost convergent to the generalized limit α if all Banach limits of x are α [2] and is denoted by f - lim x k = α.

A double sequence (x=(x_{kl})) of complex numbers is said to be almost convergent to a generalized limit L if begin{aligned} p-lim_{q,q'toinfty}sup_{m,n>0} Bigglvert frac{1}{(q+1)(q'+1)}sum_{k=m}^{m+q}sum _{l=n}^{n+q'}x_{kl}-L Biggrvert =0.

The Tweedie convergence theorem, mentioned in the context of this limiting behaviour above, could be viewed as a kind of generalized Central Limit Theorem.

The size of the population with general MCI limits the generalized use of biomarkers or therapies and shows the need for more specificity in identification of the target population.

In 1887 Markov's teacher Pafnuty Chebyshev outlined a proof of a generalized central limit theorem.

generalized central limit theorem.

Fractional ADEs are ergodic equations since they occur when a generalized central limit theorem is employed.

The micro to meso and meso to macro scale homogenization is handled with generalized central limit theorems.