Measure, Integration & Real Analysis · Problem 6C.9

Banach Spaces — Sheldon Axler

Mathematics — Measure Theory · continuous-functions-l1-norm-not-banach

Problem

Show that the vector space

C([0,1])

of continuous functions from

[0,1]

\mathbf{F}

with the norm defined by

\|f\| = \int_0^1 |f|

is not a Banach space.