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- Q1568811 subject Q8266681.
- Q1568811 subject Q8851985.
- Q1568811 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.".
- Q1568811 wikiPageExternalLink 1206.5449.
- Q1568811 wikiPageExternalLink ?op=getobj&from=objects&id=4014.
- Q1568811 wikiPageExternalLink www.encyclopediaofmath.org.
- Q1568811 wikiPageExternalLink Jordan_decomposition_(of_a_signed_measure).
- Q1568811 wikiPageWikiLink Q1130535.
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- Q1568811 wikiPageWikiLink Q40.
- Q1568811 wikiPageWikiLink Q709149.
- Q1568811 wikiPageWikiLink Q8266681.
- Q1568811 wikiPageWikiLink Q84552.
- Q1568811 wikiPageWikiLink Q8851985.
- Q1568811 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. ".
- Q1568811 label "Hahn decomposition theorem".