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- Extreme_point abstract "In mathematics, an extreme point of a convex set S in a real vector space is a point in S which does not lie in any open line segment joining two points of S. Intuitively, an extreme point is a "vertex" of S. The Krein–Milman theorem states that if S is convex and compact in a locally convex space, then S is the closed convex hull of its extreme points: In particular, such a set has extreme points.The Krein–Milman theorem is stated for locally convex topological vector spaces. The next theorems are stated for Banach spaces with the Radon–Nikodym property: A theorem of Joram Lindenstrauss states that, in a Banach space with the Radon–Nikodym property, a closed and bounded set has an extreme point. (In infinite-dimensional spaces, the property of compactness is stronger than the joint properties of being closed and being bounded). A theorem of Gerald Edgar states that, in a Banach space with the Radon–Nikodym property, a closed and bounded set is the closed convex hull of its extreme points.Edgar's theorem implies Lindenstrauss's theorem.".
- Extreme_point thumbnail Extreme_points.svg?width=300.
- Extreme_point wikiPageExternalLink extremepoint.html.
- Extreme_point wikiPageID "454968".
- Extreme_point wikiPageLength "3602".
- Extreme_point wikiPageOutDegree "24".
- Extreme_point wikiPageRevisionID "609503320".
- Extreme_point wikiPageWikiLink Banach_space.
- Extreme_point wikiPageWikiLink Bochner_integral.
- Extreme_point wikiPageWikiLink Bounded_set.
- Extreme_point wikiPageWikiLink Category:Convex_geometry.
- Extreme_point wikiPageWikiLink Category:Convex_hulls.
- Extreme_point wikiPageWikiLink Category:Functional_analysis.
- Extreme_point wikiPageWikiLink Category:Mathematical_analysis.
- Extreme_point wikiPageWikiLink Choquet_theory.
- Extreme_point wikiPageWikiLink Closed_set.
- Extreme_point wikiPageWikiLink Compact_space.
- Extreme_point wikiPageWikiLink Convex_hull.
- Extreme_point wikiPageWikiLink Convex_set.
- Extreme_point wikiPageWikiLink Dictionary_of_Algorithms_and_Data_Structures.
- Extreme_point wikiPageWikiLink Dictionary_of_algorithms_and_data_structures.
- Extreme_point wikiPageWikiLink Gerald_Edgar.
- Extreme_point wikiPageWikiLink HarperCollins.
- Extreme_point wikiPageWikiLink Harper_Collins.
- Extreme_point wikiPageWikiLink Joram_Lindenstrauss.
- Extreme_point wikiPageWikiLink Krein–Milman_theorem.
- Extreme_point wikiPageWikiLink Line_segment.
- Extreme_point wikiPageWikiLink Locally_convex_space.
- Extreme_point wikiPageWikiLink Locally_convex_topological_vector_space.
- Extreme_point wikiPageWikiLink Mathematics.
- Extreme_point wikiPageWikiLink National_Institute_of_Standards_and_Technology.
- Extreme_point wikiPageWikiLink National_institute_of_standards_and_technology.
- Extreme_point wikiPageWikiLink Radon–Nikodym_property.
- Extreme_point wikiPageWikiLink Vector_space.
- Extreme_point wikiPageWikiLink File:Extreme_points.svg.
- Extreme_point wikiPageWikiLinkText "Extreme point".
- Extreme_point wikiPageWikiLinkText "extreme point".
- Extreme_point hasPhotoCollection Extreme_point.
- Extreme_point wikiPageUsesTemplate Template:Cite_encyclopedia.
- Extreme_point wikiPageUsesTemplate Template:Cite_web.
- Extreme_point wikiPageUsesTemplate Template:Other_uses.
- Extreme_point subject Category:Convex_geometry.
- Extreme_point subject Category:Convex_hulls.
- Extreme_point subject Category:Functional_analysis.
- Extreme_point subject Category:Mathematical_analysis.
- Extreme_point hypernym Point.
- Extreme_point type Place.
- Extreme_point type Field.
- Extreme_point type Function.
- Extreme_point comment "In mathematics, an extreme point of a convex set S in a real vector space is a point in S which does not lie in any open line segment joining two points of S. Intuitively, an extreme point is a "vertex" of S. The Krein–Milman theorem states that if S is convex and compact in a locally convex space, then S is the closed convex hull of its extreme points: In particular, such a set has extreme points.The Krein–Milman theorem is stated for locally convex topological vector spaces.".
- Extreme_point label "Extreme point".
- Extreme_point sameAs Extremalpunkt.
- Extreme_point sameAs Punto_estremale.
- Extreme_point sameAs 極点.
- Extreme_point sameAs m.011bb7rh.
- Extreme_point sameAs Q1385465.
- Extreme_point sameAs Q1385465.
- Extreme_point wasDerivedFrom Extreme_point?oldid=609503320.
- Extreme_point depiction Extreme_points.svg.
- Extreme_point isPrimaryTopicOf Extreme_point.