This is an announcement for the paper "The Banach-Saks Property of the Banach product spaces" by Zhenglu Jiang and Xiaoyong Fu. Abstract: In this paper we first take a detail survey of the study of the Banach-Saks property of Banach spaces and then show the Banach-Saks property of the product spaces generated by a finite number of Banach spaces having the Banach-Saks property. A more general inequality for integrals of a class of composite functions is also given by using this property. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20, 40H05, 40G05, 47F05 Remarks: 6 The source file(s), bs0206.tex: 25085 bytes, is(are) stored in gzipped form as 0702538.gz with size 8kb. The corresponding postcript file has gzipped size 91kb. Submitted from: mcsjzl@mail.sysu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0702538 or http://arXiv.org/abs/math.FA/0702538 or by email in unzipped form by transmitting an empty message with subject line uget 0702538 or in gzipped form by using subject line get 0702538 to: math@arXiv.org.