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Throughout this paper,let(Ω,ι,μ)be a probability space,D the collection of allleft-continuous distribution functions,and D~+={F(0)=0|F∈D},and L(Ω)the collec-tion of all random variables which is a.s.finite on Ω,and L~+={ξ≥0 a.s.|ξ∈L(Ω)}.For random metric