Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Dini's_theorem> ?p ?o. }
Showing items 1 to 35 of
35
with 100 items per page.
- Dini's_theorem abstract "In the mathematical field of analysis, Dini's theorem states that if X is a compact topological space, and { fn } is a monotonically increasing sequence (meaning fn(x) ≤ fn+1(x) for all n and x) of continuous real-valued functions on X which converges pointwise to a continuous function f, then the convergence is uniform. The same conclusion holds if { fn } is monotonically decreasing instead of increasing. The theorem is named after Ulisse Dini.This is one of the few situations in mathematics where pointwise convergence implies uniform convergence; the key is the greater control implied by the monotonicity. Note also that the limit function must be continuous, since a uniform limit of continuous functions is necessarily continuous. (if the limit function is not required to be continuous, the theorem doesn't hold, as seen by the sequence fn(x) = xn over [0,1]).".
- Dini's_theorem wikiPageID "9177825".
- Dini's_theorem wikiPageRevisionID "589674859".
- Dini's_theorem hasPhotoCollection Dini's_theorem.
- Dini's_theorem subject Category:Articles_containing_proofs.
- Dini's_theorem subject Category:Theorems_in_real_analysis.
- Dini's_theorem type Abstraction100002137.
- Dini's_theorem type Communication100033020.
- Dini's_theorem type Message106598915.
- Dini's_theorem type Proposition106750804.
- Dini's_theorem type Statement106722453.
- Dini's_theorem type Theorem106752293.
- Dini's_theorem type TheoremsInRealAnalysis.
- Dini's_theorem comment "In the mathematical field of analysis, Dini's theorem states that if X is a compact topological space, and { fn } is a monotonically increasing sequence (meaning fn(x) ≤ fn+1(x) for all n and x) of continuous real-valued functions on X which converges pointwise to a continuous function f, then the convergence is uniform. The same conclusion holds if { fn } is monotonically decreasing instead of increasing.".
- Dini's_theorem label "Dini's theorem".
- Dini's_theorem label "Lemma di Dini".
- Dini's_theorem label "Satz von Dini".
- Dini's_theorem label "Stelling van Dini".
- Dini's_theorem label "Teorema de Dini".
- Dini's_theorem label "Théorèmes de Dini".
- Dini's_theorem label "Twierdzenie Diniego".
- Dini's_theorem label "Теорема Дини".
- Dini's_theorem label "迪尼定理".
- Dini's_theorem sameAs Satz_von_Dini.
- Dini's_theorem sameAs Théorèmes_de_Dini.
- Dini's_theorem sameAs Lemma_di_Dini.
- Dini's_theorem sameAs Stelling_van_Dini.
- Dini's_theorem sameAs Twierdzenie_Diniego.
- Dini's_theorem sameAs Teorema_de_Dini.
- Dini's_theorem sameAs m.027_9mn.
- Dini's_theorem sameAs Q595466.
- Dini's_theorem sameAs Q595466.
- Dini's_theorem sameAs Dini's_theorem.
- Dini's_theorem wasDerivedFrom Dini's_theorem?oldid=589674859.
- Dini's_theorem isPrimaryTopicOf Dini's_theorem.