Examples of normed spaces
- The Euclidean space endowed with the Euclidean norm for all . This is the canonical example of a finite dimensional vector space; in fact all finite dimensional real normed spaces of dimension n are isomorphic to this space and, indeed, to one another.
- The space of the equivalence class of all real valued bounded Lebesgue measurable functions on the interval [0,1] with the norm . This is an example of an infinite dimensional normed space.