Matches in DBpedia 2016-04 for { ?s ?p "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. "@en }
Showing triples 1 to 2 of
2
with 100 triples per page.
- 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. ".
- 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. ".