# Minkowski inequality

If $p\geq 1$ and $a_{k},b_{k}$ are real numbers for $k=1,\ldots$, then

 $\left(\sum_{k=1}^{n}|a_{k}+b_{k}|^{p}\right)^{1/p}\leq\left(\sum_{k=1}^{n}|a_{% k}|^{p}\right)^{1/p}+\left(\sum_{k=1}^{n}|b_{k}|^{p}\right)^{1/p}$

The Minkowski inequality is in fact valid for all $L^{p}$ norms with $p\geq 1$ on arbitrary measure spaces. This covers the case of $\mathbbmss{R}^{n}$ listed here as well as spaces of sequences and spaces of functions, and also complex $L^{p}$ spaces.

Title Minkowski inequality MinkowskiInequality 2013-03-22 11:46:24 2013-03-22 11:46:24 drini (3) drini (3) 13 drini (3) Theorem msc 26D15 LebesgueMeasure MeasurableSpace