A direct proof of F. Riesz representation Theorem
classification
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theoremproofrieszdirectrepresentationactingargumentsavoids
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A direct proof of the Riesz representation theorem is provided. This theorem characterizes the linear functionals acting on the vector space $C(K)$ of continuous functions defined on a compact subset $K$ of the real numbers $\mathbb{R}$. This proof avoids complicated arguments commonly used in generalizations of Riesz original theorem.
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