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Minkowski Integral Inequality

If $p>1$, then

\left[{\int_a^b \vert f(x)+g(x)\vert^p\,dx}\right]^{1/p} \le...]^{1/p}+\left[{\int_a^b \vert g(x)\vert^p\,dx}\right]^{1/p}.

See also Minkowski Sum Inequality


Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 11, 1972.

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1099, 1993.

Hardy, G. H.; Littlewood, J. E.; and Pólya, G. Inequalities, 2nd ed. Cambridge, England: Cambridge University Press, pp. 146-150, 1988.

Minkowski, H. Geometrie der Zahlen, Vol. 1. Leipzig, Germany: pp. 115-117, 1896.

Sansone, G. Orthogonal Functions, rev. English ed. New York: Dover, p. 33, 1991.

© 1996-9 Eric W. Weisstein