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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.

  • 1
    Two links that will help: 1. [Riesz representation theorem](http://en.wikipedia.org/wiki/Riesz_representation_theorem#The_representation_theorem_for_linear_functionals_on_Cc.28X.29) 2. [Riemann-Stieltjes integral](http://en.wikipedia.org/wiki/Riemann-Stieltjes_integral#Application_to_functional_analysis)2012-11-08
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    Look up the Riesz representation theorem.2012-11-08

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