Measure, Integration & Real Analysis · Problem 8C.13

Real and Complex Measures — Sheldon Axler

Mathematics — Measure Theory · separability-hilbert-spaces

Problem

(a) Show that the Hilbert space

L^2([0,1])

is separable. (b) Show that the Hilbert space

L^2(\mathbf{R})

is separable. (c) Show that the Banach space

\ell^\infty

is not separable.