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- Hahn_decomposition_theorem abstract "In mathematics, the Hahn decomposition theorem, named after the Austrian mathematician Hans Hahn, states that given a measurable space (X,Σ) and a signed measure μ defined on the σ-algebra Σ, there exist two measurable sets P and N in Σ such that:P ∪ N = X and P ∩ N = ∅.For each E in Σ such that E ⊆ P one has μ(E) ≥ 0; that is, P is a positive set for μ.For each E in Σ such that E ⊆ N one has μ(E) ≤ 0; that is, N is a negative set for μ.Moreover, this decomposition is essentially unique, in the sense that for any other pair (P', N') of measurable sets fulfilling the above three conditions, the symmetric differences P Δ P' and N Δ N' are μ-null sets in the strong sense that every measurable subset of them has zero measure. The pair (P,N) is called a Hahn decomposition of the signed measure μ.".
- Hahn_decomposition_theorem wikiPageExternalLink 1206.5449.
- Hahn_decomposition_theorem wikiPageExternalLink ?op=getobj&from=objects&id=4014.
- Hahn_decomposition_theorem wikiPageExternalLink www.encyclopediaofmath.org.
- Hahn_decomposition_theorem wikiPageExternalLink Jordan_decomposition_(of_a_signed_measure).
- Hahn_decomposition_theorem wikiPageID "2985858".
- Hahn_decomposition_theorem wikiPageLength "8175".
- Hahn_decomposition_theorem wikiPageOutDegree "19".
- Hahn_decomposition_theorem wikiPageRevisionID "646833846".
- Hahn_decomposition_theorem wikiPageWikiLink Austria.
- Hahn_decomposition_theorem wikiPageWikiLink Category:Articles_containing_proofs.
- Hahn_decomposition_theorem wikiPageWikiLink Category:Theorems_in_measure_theory.
- Hahn_decomposition_theorem wikiPageWikiLink Hans_Hahn_(mathematician).
- Hahn_decomposition_theorem wikiPageWikiLink Infimum_and_supremum.
- Hahn_decomposition_theorem wikiPageWikiLink Mathematical_induction.
- Hahn_decomposition_theorem wikiPageWikiLink Mathematician.
- Hahn_decomposition_theorem wikiPageWikiLink Mathematics.
- Hahn_decomposition_theorem wikiPageWikiLink Null_set.
- Hahn_decomposition_theorem wikiPageWikiLink PlanetMath.
- Hahn_decomposition_theorem wikiPageWikiLink Positive_and_negative_sets.
- Hahn_decomposition_theorem wikiPageWikiLink Q.E.D..
- Hahn_decomposition_theorem wikiPageWikiLink Series_(mathematics).
- Hahn_decomposition_theorem wikiPageWikiLink Sigma-algebra.
- Hahn_decomposition_theorem wikiPageWikiLink Sigma_additivity.
- Hahn_decomposition_theorem wikiPageWikiLink Signed_measure.
- Hahn_decomposition_theorem wikiPageWikiLink Symmetric_difference.
- Hahn_decomposition_theorem wikiPageWikiLink Universal_property.
- Hahn_decomposition_theorem wikiPageWikiLinkText "Hahn decomposition theorem".
- Hahn_decomposition_theorem wikiPageWikiLinkText "Hahn decomposition".
- Hahn_decomposition_theorem wikiPageWikiLinkText "Hahn–Jordan decomposition".
- Hahn_decomposition_theorem wikiPageWikiLinkText "Hahn-Jordan decomposition".
- Hahn_decomposition_theorem wikiPageWikiLinkText "Jordan decomposition of a measure".
- Hahn_decomposition_theorem wikiPageWikiLinkText "Jordan decomposition".
- Hahn_decomposition_theorem wikiPageWikiLinkText "Jordan's decomposition theorem".
- Hahn_decomposition_theorem id "p/h046140".
- Hahn_decomposition_theorem title "Hahn decomposition".
- Hahn_decomposition_theorem wikiPageUsesTemplate Template:Cite_arXiv.
- Hahn_decomposition_theorem wikiPageUsesTemplate Template:Cite_book.
- Hahn_decomposition_theorem wikiPageUsesTemplate Template:Springer.
- Hahn_decomposition_theorem subject Category:Articles_containing_proofs.
- Hahn_decomposition_theorem subject Category:Theorems_in_measure_theory.
- Hahn_decomposition_theorem type Proof.
- Hahn_decomposition_theorem type Theorem.
- Hahn_decomposition_theorem comment "In mathematics, the Hahn decomposition theorem, named after the Austrian mathematician Hans Hahn, states that given a measurable space (X,Σ) and a signed measure μ defined on the σ-algebra Σ, there exist two measurable sets P and N in Σ such that:P ∪ N = X and P ∩ N = ∅.For each E in Σ such that E ⊆ P one has μ(E) ≥ 0; that is, P is a positive set for μ.For each E in Σ such that E ⊆ N one has μ(E) ≤ 0; that is, N is a negative set for μ.Moreover, this decomposition is essentially unique, in the sense that for any other pair (P', N') of measurable sets fulfilling the above three conditions, the symmetric differences P Δ P' and N Δ N' are μ-null sets in the strong sense that every measurable subset of them has zero measure. ".
- Hahn_decomposition_theorem label "Hahn decomposition theorem".
- Hahn_decomposition_theorem sameAs Q1568811.
- Hahn_decomposition_theorem sameAs Hahn-Jordan-Zerlegung.
- Hahn_decomposition_theorem sameAs Teorema_di_decomposizione_di_Hahn.
- Hahn_decomposition_theorem sameAs ハーンの分解定理.
- Hahn_decomposition_theorem sameAs Twierdzenie_Hahna_o_rozkładzie.
- Hahn_decomposition_theorem sameAs m.08htxl.
- Hahn_decomposition_theorem sameAs Q1568811.
- Hahn_decomposition_theorem wasDerivedFrom Hahn_decomposition_theorem?oldid=646833846.
- Hahn_decomposition_theorem isPrimaryTopicOf Hahn_decomposition_theorem.