Given a signed measure space (X, A, X). (a) Show that if E E A and...
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Given a signed measure space (X, A, X). (a) Show that if E E A and X(E) > 0, then there exists a subset Eo CE which is a positive set for λ with X(Eo) > X(E). (b) Show that if EEA and X(E) <0, then there exists a subset Eo CE which is a negative set for λ with X(Eo) ≤ X(E). Given a signed measure space (X, A, X). (a) Show that if E E A and X(E) > 0, then there exists a subset Eo CE which is a positive set for λ with X(Eo) > X(E). (b) Show that if EEA and X(E) <0, then there exists a subset Eo CE which is a negative set for λ with X(Eo) ≤ X(E).
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