Measure, Integration & Real Analysis · Problem 9A.3

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · total-variation-complex-measure

Problem

Suppose ν\nu is a complex measure on a measurable space (X,S)(X, \mathcal{S}). Prove that ∣ν∣(X)=ν(X)|\nu|(X) = \nu(X) if and only if ν\nu is a (positive) measure.

Related theory

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