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Igor Khavkine
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Measure theory treatment geared toward the Riesz representation theorem

I'm looking for recommendations for books (or lecture notes) that develop measure theory in sufficient detail to state and prove the Riesz representation theorem (which is the characterization of the topological duals of linear spaces of continuous functions on a completely regular topological space). In particular, I'd like to see the cases of $C(X)$ and $C_K(X)$ of all continuous functions and all compactly supported continuous functions for non-compact $X$, with the usual Fréchet and locally convex topologies, covered as well as the more common case of compact $X$.

I know that this is basically in Dunford & Schwartz, but I always find it helpful to have multiple references at hand.

Igor Khavkine
  • 21.5k
  • 2
  • 60
  • 113