equicontinuity वाक्य
उदाहरण वाक्य
मोबाइल
- In practice, showing the equicontinuity is often not so difficult.
- Note that the equicontinuity is essential here.
- Choosing a finite subcover then gives equicontinuity.
- So, given, let } } to verify the definition of equicontinuity of the sequence.
- The notion of equicontinuity was introduced in the late 19th century by the Italian mathematicians Cesare Arzel?and Giulio Ascoli.
- A typical Fredholm integral equation gives rise to a compact operator " K " on function spaces; the compactness property is shown by equicontinuity.
- One can use, for instance, Cauchy's estimate to show the equicontinuity ( on a compact subset ) and conclude that the limit is holomorphic.
- 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.
- 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.
- 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.
- *If estimator " T n " is defined implicitly, for example as a value that maximizes certain objective function ( see extremum estimator ), then a more complicated argument involving stochastic equicontinuity has to be used.
- Equicontinuity appears in the formulation of Ascoli's theorem, which states that a subset of " C " ( " X " ), the space of continuous functions on a compact Hausdorff space " X ", is compact if and only if it is closed, pointwise bounded and equicontinuous.
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