Let $a < b,$ $[a,b]$ be a closed real interval and let $f:[a,b]\to\mathbb R$ be a Riemann-integrable function. Then
$$||f||_p:=\left(\int_a^b|f(x)|^p dx\right)^{1/p}$$
defines a norm on the vector space of all Riemann-integrable functions defined on the interval $[a,b].$
Proofs: 1
Proofs: 1 2 3
Propositions: 4 5 6
