Abstract: By employing the structure of P-sets，this paper presents the confidence characteristic of element transfer，the confidence characteristic of attribute set α of internal P-sets and the confidence characteristic of attribute set α of outer P-sets.Then by employing the above results，this paper gives the confidence characteristic of internal P-sets and outer P-sets，and proposes the stochastic structure and the stochastic theorem of internal P-sets and outer P-sets.The structure of cantor’s sets is the special case of the stochastic structure of P-sets，while the latter is the general form of the former.