This paper presents a unified view of interestingness measures for interesting pattern discovery. Specifically, we first provide three necessary conditions for interestingness measures being used for association pattern discovery. Then, we reveal one desirable property for interestingness measures: the support-ascending conditional antimonotone property (SA-CAMP). Along this line, we prove that the measures possessing SA-CAMP are suitable for pattern discovery if the itemset-traversal structure is defined by a support-ascending set enumeration tree. In addition, we provide a thorough study on the family of the generalized mean (GM) measure and show their appealing properties, which are exploited for developing the GMiner algorithm for finding interesting association patterns. Finally, experimental results show that GMiner can efficiently identify interesting patterns based on SA-CAMP of the GM measure, even at an extremely low level of support.