In its lawsuit, Apple accused Amazon of misusing the "app store" name in connection with the sales of apps for Android devices and the Kindle Fire.
Amazon countered that the term "app store" had become so generic that using it would not mislead customers.
Earlier this year, US District Judge Phyllis Hamilton ruled that Apple had failed to establish that Amazon made any false statement or had deceived customers.
The case is Apple Inc v. Amazon.com Inc et al, U.S. District Court, Northern District of California, No. 11-01327.