A direct proof of F. Riesz representation Theorem
  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. 
Rafael del Rio, Asaf Franco, Jose Lara
math.FA