Category:Minkowski's Inequality for Integrals

This category contains pages concerning Minkowski's Inequality for Integrals:

Let $f, g$ be (Darboux) integrable functions.

Let $p \in \R$ such that $p > 1$.

Then:

$\ds \paren {\int_a^b \size {\map f x + \map g x}^p \rd x}^{1/p} \le \paren {\int_a^b \size {\map f x}^p \rd x}^{1 / p} + \paren {\int_a^b \size {\map g x}^p \rd x}^{1 / p}$

Source of Name

This entry was named for Hermann Minkowski.