Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Created:
If X is a set, M is a σ-algebra on X, and μ is a signed measure, i.e., a countably additive functional M→R, then μ is bounded and there is S∈M such that
μ(m)≥0 for every m∈M such that m⊂S;
μ(m)≤0 for every m∈M such that m∩S=∅.
A standard theorem present in many introductory textbooks. See, for example, Theorem 231E in Fremlin’s Measure Theory.
1 to 1 of 1