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I am stuck in this problem.

Describe the dual space of $C[0,1]$, where $C[0,1]$ is the Banach space of all real continuous functions on $[0,1]$ induced norm $$ \|x\|_{\max}=\sup_{t\in [0,1]}|x(t)|\quad \forall x\in C[0,1]. $$

Thank you for all helping.

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Two links that will help: 1. Riesz representation theorem 2. Riemann-Stieltjes integral –  user48624 Nov 8 '12 at 8:33
    
Look up the Riesz representation theorem. –  copper.hat Nov 8 '12 at 8:33

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