Abstract: P-sets are a set pair which are composed of internal P-sets XF and outer P-set sXl'，or (XF，XF ) is P-sets. P-sets have dynamic characteristics. 13y using P-sets, the concept of Information Inheritance and Information Inheritance Metric,as well as Information Inheritance Theorems were given. Based on characteristic of Information Inheritance,method and application of information state identification were proposed. Information Image-generation, applications of Information Image hidden-potential were provided. P-sets arc new theory and method to study dynamic information system. Finally, the reality of P-sets was given,the differences of P-sets and Z. Pawlak rough sets were given.

Key words: P-sets, Information inheritance, Basic number circle theorem, Information state identification, Information image hidden-potential, Applications