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Proposition: Minkowski's Inequality for Integral p-norms

Let $[a,b]$ be a closed real interval, $p\ge 1$ be a real number and let $f,g:[a,b]\to\mathbb R$ be two Riemann-integrable functions. The for the integral p-norms the Minkowski's inequality holds:

$$||f+g||_p\le ||f||_p+||g||_p,\quad\forall p\ge 1.$$

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References

Bibliography

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