Measure, Integration & Real Analysis · Problem 6D.2

L^p Spaces — Sheldon Axler

Mathematics — Measure Theory · linear-functionals-null-space

Problem

Suppose

\varphi

is a linear functional on a vector space

V

. Prove that if

U

is a subspace of

V

such that

\operatorname{null} \varphi \subseteq U

, then

U = \operatorname{null} \varphi

U = V