# Inheriting Inequality

### Problem

### Solution

The answer is, Yes, and follows from *Karamata's theorem*. The sequences can be so rearranged as to satisfy *Karamata's majorization* requirement. Since the function $f(x)=x^p$ is convex and strictly increasing for $p\gt 1$ Karamata's theorem applies to establish $\displaystyle \sum_{k=1}^na_k^p\ge\sum_{k=1}^nb_k^p.$

### Acknowledgment

The question arose following N.N. Taleb's similar inquiry with $p\lt 1.$

|Contact| |Front page| |Contents| |Algebra|

Copyright © 1996-2018 Alexander Bogomolny