Question

State and prove hahn decomposition theorem.

Answer 1

The Hahn Decomposition Theorem states that if Σ is a σ-algebra (or a σ-ring), and µ : Σ → [−∞, ∞) is a signed measure, then there exist a positive set A and a negative set B in Σ such that A ∩ B = ∅ and X = A ∪ B.

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