Proposition: Integral p-Norm

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


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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983