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- Equicontinuity abstract "In mathematical analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood, in a precise sense described herein. In particular, the concept applies to countable families, and thus sequences of functions.The 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. As a corollary, a sequence in C(X) is uniformly convergent if and only if it is equicontinuous and converges pointwise to a function (not necessarily continuous a-priori). In particular, the limit of an equicontinuous pointwise convergent sequence of continuous functions fn on either metric space or locally compact space is continuous. If, in addition, fn are holomorphic, then the limit is also holomorphic.The uniform boundedness principle states that a pointwise bounded family of continuous linear operators between Banach spaces is equicontinuous.".
- Equicontinuity wikiPageID "460642".
- Equicontinuity wikiPageLength "13584".
- Equicontinuity wikiPageOutDegree "35".
- Equicontinuity wikiPageRevisionID "674722251".
- Equicontinuity wikiPageWikiLink Academic_Press.
- Equicontinuity wikiPageWikiLink Analytic_function.
- Equicontinuity wikiPageWikiLink Arzelà–Ascoli_theorem.
- Equicontinuity wikiPageWikiLink Banach_space.
- Equicontinuity wikiPageWikiLink Banach–Alaoglu_theorem.
- Equicontinuity wikiPageWikiLink Barrelled_space.
- Equicontinuity wikiPageWikiLink Category:Continuous_mappings.
- Equicontinuity wikiPageWikiLink Category:Mathematical_analysis.
- Equicontinuity wikiPageWikiLink Continuous_function.
- Equicontinuity wikiPageWikiLink Continuous_functions_on_a_compact_Hausdorff_space.
- Equicontinuity wikiPageWikiLink Convergence_of_random_variables.
- Equicontinuity wikiPageWikiLink Countable_set.
- Equicontinuity wikiPageWikiLink Filter_(mathematics).
- Equicontinuity wikiPageWikiLink Heine–Borel_theorem.
- Equicontinuity wikiPageWikiLink Julia_set.
- Equicontinuity wikiPageWikiLink Lipschitz_continuity.
- Equicontinuity wikiPageWikiLink Mathematical_analysis.
- Equicontinuity wikiPageWikiLink McGraw-Hill_Education.
- Equicontinuity wikiPageWikiLink Mean_value_theorem.
- Equicontinuity wikiPageWikiLink Metric_space.
- Equicontinuity wikiPageWikiLink Neighbourhood_(mathematics).
- Equicontinuity wikiPageWikiLink Random_variable.
- Equicontinuity wikiPageWikiLink Sign_function.
- Equicontinuity wikiPageWikiLink Taylors_theorem.
- Equicontinuity wikiPageWikiLink Topological_space.
- Equicontinuity wikiPageWikiLink Topological_vector_space.
- Equicontinuity wikiPageWikiLink Uniform_boundedness_principle.
- Equicontinuity wikiPageWikiLink Uniform_continuity.
- Equicontinuity wikiPageWikiLink Uniform_norm.
- Equicontinuity wikiPageWikiLink Uniform_space.
- Equicontinuity wikiPageWikiLinkText "Equicontinuity".
- Equicontinuity wikiPageWikiLinkText "equicontinuity".
- Equicontinuity wikiPageWikiLinkText "equicontinuous families".
- Equicontinuity wikiPageWikiLinkText "equicontinuous".
- Equicontinuity id "p/e035990".
- Equicontinuity title "Equicontinuity".
- Equicontinuity wikiPageUsesTemplate Template:Citation.
- Equicontinuity wikiPageUsesTemplate Template:Citation_needed.
- Equicontinuity wikiPageUsesTemplate Template:Main.
- Equicontinuity wikiPageUsesTemplate Template:Mset.
- Equicontinuity wikiPageUsesTemplate Template:Norm.
- Equicontinuity wikiPageUsesTemplate Template:Springer.
- Equicontinuity subject Category:Continuous_mappings.
- Equicontinuity subject Category:Mathematical_analysis.
- Equicontinuity type Field.
- Equicontinuity type Function.
- Equicontinuity type Mapping.
- Equicontinuity comment "In mathematical analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood, in a precise sense described herein.".
- Equicontinuity label "Equicontinuity".
- Equicontinuity sameAs Q249092.
- Equicontinuity sameAs Equicontinuïtat.
- Equicontinuity sameAs Gleichgradige_Stetigkeit.
- Equicontinuity sameAs Equicontinuidad.
- Equicontinuity sameAs Équicontinuité.
- Equicontinuity sameAs רציפות_במידה_אחידה.
- Equicontinuity sameAs Equicontinuità.
- Equicontinuity sameAs 同程度連続.
- Equicontinuity sameAs 동등_연속_함수족.
- Equicontinuity sameAs Equicontinuidade.
- Equicontinuity sameAs m.02c8gk.
- Equicontinuity sameAs Равностепенная_непрерывность.
- Equicontinuity sameAs Рівностепенева_неперервність.
- Equicontinuity sameAs Liên_tục_đồng_bậc.
- Equicontinuity sameAs Q249092.
- Equicontinuity sameAs 等度连续.
- Equicontinuity wasDerivedFrom Equicontinuity?oldid=674722251.
- Equicontinuity isPrimaryTopicOf Equicontinuity.