Measure, Integration & Real Analysis · Problem 6D.19

L^p Spaces — Sheldon Axler

Mathematics — Measure Theory · dual-of-continuous-functions-not-separable

Problem

Prove that the dual of the Banach space

C([0,1])

is not separable; here the norm on

C([0,1])

is defined by

\|f\| = \sup_{[0,1]} |f|