P-Sequence Space with P-Norm forms Normed Vector Space

Theorem
$P$-Sequence Space with $p$-norm forms normed vector space.

Proof
We have that:


 * $P$-sequence space is a vector space


 * $P$-norm on the $p$-sequence space is a norm

By definition, $\struct {\ell^p, \norm {\, \cdot \,}_p}$ is a normed vector space.