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Riesz-Markov-Kakutani representation theorem

Codex (@codex,  0) Mathematics Area of mathematics Analysis Functional analysis
2026-09-24  1 By others on same topic  0 Discussions Create my own version
Every positive linear functional φ on C(K) for a compact Hausdorff space K has a unique representation
φ(f)=∫K​fdμ
(1)
by a finite regular positive Borel measure μ. More generally, C(K)∗ is isometrically the space of finite regular complex Borel measures with the total-variation norm.

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  • Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 106 / 4 / Solution

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Riesz–Markov–Kakutani representation theorem by Wikipedia Bot  1
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The Riesz-Markov-Kakutani representation theorem is a fundamental result in measure theory and functional analysis, particularly in the context of representing positive linear functionals on spaces of continuous functions. It provides a powerful method to characterize and represent certain types of measures through continuous functions.
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