In practice, showing the equicontinuity is often not so difficult.
2.
Note that the equicontinuity is essential here.
3.
Choosing a finite subcover then gives equicontinuity.
4.
So, given, let } } to verify the definition of equicontinuity of the sequence.
5.
The notion of equicontinuity was introduced in the late 19th century by the Italian mathematicians Cesare Arzel?and Giulio Ascoli.
6.
A typical Fredholm integral equation gives rise to a compact operator " K " on function spaces; the compactness property is shown by equicontinuity.
7.
One can use, for instance, Cauchy's estimate to show the equicontinuity ( on a compact subset ) and conclude that the limit is holomorphic.
8.
For instance, stochastic equicontinuity, along with other conditions, can be used to show uniform weak convergence, which can be used to prove the convergence of extremum estimators.
9.
The most general scenario in which equicontinuity can be defined is for topological spaces whereas " uniform " equicontinuity requires the filter of neighbourhoods of one point to be somehow comparable with the filter of neighbourhood of another point.
10.
The most general scenario in which equicontinuity can be defined is for topological spaces whereas " uniform " equicontinuity requires the filter of neighbourhoods of one point to be somehow comparable with the filter of neighbourhood of another point.
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