Abstract: Based on the conception of P_(ρ,σ)-set(X^P-F_ρ, X^PF_σ), this paper studied the relation between outer P_(ρ,σ)-set and outer P-set: give outer P_(ρ,σ)-set and outer P-set relation theorem, outer P_(ρ,σ)-set and numerical value σ relation theorem, outer P_(ρ,σ)-set’s range; studied other characteristics of outer P(ρ,σ)-set: give the finiteness theorem of outer P_(ρ,σ)-set, the set chain theorem of outer P_(ρ,σ)-set, the outer P_(ρ,σ)-set probability interval finite partition theorem, and its corollary; also give generation, reduction, identification theorem of outer P_(ρ,σ)-set, filter generation theorem of outer P_(ρ,σ)-set; finally give its application. 

Key words: P-set, outer P_(ρ,σ)-set, finiteness, finite partition, probability