#### Document Type

Article

#### Abstract

A moment inequality is proved for sums of independent random variables in the Lorentz spaces LPtq, thus extending an inequality of Rosenthal. The latter result is used in combination with a square function inequality to give a proof of a Banach space isomorphism theorem. Further moment inequalities are also proved.

#### Publication Info

Published in *Proceedings of the American Mathematical Society*, Volume 104, Issue 1, 1988, pages 221-226.

First published in Proceedings of the American Mathematical Society in 1988, published by the American Mathematical Society.

Carothers, N. L., & Dilworth, S. J. (1988). Inequalities for Sums of Independent Random Variables. *Proceedings of the American Mathematical Society, 104* (1), 221-226.